04_7_construct_figuretable_test_linear_linear_optimal_iv

Load

Estimation

linear-demand linear-cost, \(\sigma = 1\)

\(\theta = 0.05\)

\(\alpha_2 = 0.1\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.817	1.000	7.959	9.580	15.288
alpha1_hat	100	0	0.825	0.857	−1.470	0.766	3.413
alpha2_hat	100	0	0.110	0.081	−0.105	0.109	0.348
alpha3_hat	100	0	0.979	0.217	0.494	0.962	1.691
gamma0_hat	100	0	3.077	0.886	0.820	3.074	5.536
gamma1_hat	100	0	1.499	6.355	−13.374	0.682	56.754
gamma2_hat	100	0	0.774	0.141	0.455	0.774	1.072
gamma3_hat	100	0	0.780	0.169	0.438	0.771	1.227
theta_hat	100	0	−0.654	3.777	−33.399	−0.165	9.249
theta_hat_t_stats	100	0	−0.418	1.124	−3.264	−0.307	2.625
R2_demand	100	0	0.370	0.292	−1.623	0.433	0.715
R2_supply	100	0	0.983	0.004	0.970	0.984	0.991

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.978	0.748	8.375	9.847	12.592
alpha1_hat	100	0	0.829	0.670	−0.830	0.745	2.707
alpha2_hat	100	0	0.116	0.061	−0.056	0.113	0.304
alpha3_hat	100	0	0.999	0.167	0.570	0.990	1.613
gamma0_hat	100	0	2.139	0.901	−0.193	2.333	4.099
gamma1_hat	100	0	0.658	1.834	−11.212	0.939	4.612
gamma2_hat	100	0	0.872	0.144	0.545	0.852	1.269
gamma3_hat	100	0	0.873	0.132	0.563	0.859	1.217
theta_hat	100	0	0.024	0.892	−1.713	−0.073	5.346
theta_hat_t_stats	100	0	−0.171	0.971	−2.186	−0.158	2.515
R2_demand	100	0	0.325	0.241	−0.787	0.387	0.644
R2_supply	100	0	0.980	0.004	0.969	0.980	0.988

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.973	0.410	9.143	9.948	10.873
alpha1_hat	100	0	0.947	0.358	0.030	0.932	1.842
alpha2_hat	100	0	0.104	0.034	0.028	0.103	0.204
alpha3_hat	100	0	0.998	0.103	0.757	0.985	1.293
gamma0_hat	100	0	1.511	0.676	−0.463	1.639	2.851
gamma1_hat	100	0	0.865	0.907	−3.144	0.848	3.198
gamma2_hat	100	0	0.938	0.099	0.746	0.931	1.208
gamma3_hat	100	0	0.946	0.094	0.760	0.932	1.192
theta_hat	100	0	0.029	0.459	−1.402	0.076	1.969
theta_hat_t_stats	100	0	0.048	1.056	−3.335	0.239	2.741
R2_demand	100	0	0.332	0.127	−0.047	0.341	0.540
R2_supply	100	0	0.977	0.004	0.965	0.978	0.986

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.997	0.199	9.646	9.993	10.439
alpha1_hat	100	0	0.995	0.169	0.621	0.983	1.359
alpha2_hat	100	0	0.101	0.018	0.067	0.101	0.140
alpha3_hat	100	0	1.001	0.046	0.901	0.994	1.106
gamma0_hat	100	0	1.126	0.300	0.300	1.142	1.798
gamma1_hat	100	0	0.929	0.304	0.177	0.931	1.909
gamma2_hat	100	0	0.986	0.049	0.881	0.979	1.124
gamma3_hat	100	0	0.987	0.041	0.868	0.986	1.096
theta_hat	100	0	0.064	0.160	−0.460	0.068	0.510
theta_hat_t_stats	100	0	0.363	0.930	−2.190	0.402	2.791
R2_demand	100	0	0.342	0.050	0.237	0.340	0.458
R2_supply	100	0	0.975	0.002	0.970	0.975	0.980

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.996	0.146	9.640	9.993	10.428
alpha1_hat	100	0	1.012	0.118	0.683	1.016	1.274
alpha2_hat	100	0	0.099	0.011	0.073	0.099	0.124
alpha3_hat	100	0	1.000	0.037	0.909	1.002	1.081
gamma0_hat	100	0	1.095	0.203	0.589	1.098	1.581
gamma1_hat	100	0	0.926	0.242	0.351	0.933	1.440
gamma2_hat	100	0	0.989	0.031	0.913	0.989	1.076
gamma3_hat	100	0	0.993	0.026	0.925	0.995	1.053
theta_hat	100	0	0.072	0.129	−0.197	0.065	0.334
theta_hat_t_stats	100	0	0.604	1.080	−1.715	0.565	2.765
R2_demand	100	0	0.332	0.041	0.221	0.332	0.431
R2_supply	100	0	0.975	0.001	0.972	0.975	0.978

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.003	0.080	9.808	10.004	10.179
alpha1_hat	100	0	1.000	0.075	0.819	0.995	1.214
alpha2_hat	100	0	0.100	0.007	0.080	0.101	0.117
alpha3_hat	100	0	1.000	0.021	0.950	0.999	1.063
gamma0_hat	100	0	1.024	0.153	0.632	1.037	1.393
gamma1_hat	100	0	0.916	0.131	0.542	0.936	1.200
gamma2_hat	100	0	0.997	0.021	0.936	0.996	1.043
gamma3_hat	100	0	0.999	0.020	0.961	0.997	1.057
theta_hat	100	0	0.089	0.073	−0.067	0.082	0.319
theta_hat_t_stats	100	0	1.185	0.961	−0.962	1.132	4.005
R2_demand	100	0	0.336	0.022	0.287	0.336	0.389
R2_supply	100	0	0.975	0.001	0.972	0.975	0.977

\(\alpha_2 = 0.5\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.059	1.165	7.650	9.738	14.910
alpha1_hat	100	0	1.176	1.935	−3.982	1.278	7.462
alpha2_hat	100	0	0.490	0.207	0.124	0.465	1.534
alpha3_hat	100	0	0.985	0.246	0.477	0.942	1.737
gamma0_hat	100	0	3.015	0.997	0.487	3.036	5.063
gamma1_hat	100	0	0.263	2.408	−5.489	0.308	8.755
gamma2_hat	100	0	0.781	0.175	0.384	0.780	1.432
gamma3_hat	100	0	0.780	0.159	0.356	0.787	1.298
theta_hat	100	0	−0.101	0.418	−1.075	−0.126	0.836
theta_hat_t_stats	100	0	−0.397	1.096	−3.247	−0.373	1.804
R2_demand	100	0	0.458	0.301	−1.023	0.537	0.783
R2_supply	100	0	0.977	0.005	0.961	0.977	0.989

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.954	0.651	8.636	9.896	11.753
alpha1_hat	100	0	1.072	1.230	−1.860	1.047	3.562
alpha2_hat	100	0	0.486	0.131	0.170	0.479	0.855
alpha3_hat	100	0	1.000	0.157	0.639	0.996	1.408
gamma0_hat	100	0	2.018	0.744	−0.096	2.122	3.772
gamma1_hat	100	0	0.610	1.432	−3.065	0.705	5.362
gamma2_hat	100	0	0.891	0.113	0.599	0.894	1.243
gamma3_hat	100	0	0.886	0.121	0.583	0.890	1.197
theta_hat	100	0	−0.023	0.257	−0.936	−0.033	0.540
theta_hat_t_stats	100	0	−0.168	0.971	−2.766	−0.150	1.607
R2_demand	100	0	0.513	0.142	0.085	0.535	0.744
R2_supply	100	0	0.972	0.005	0.956	0.972	0.981

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.044	0.566	8.881	10.032	11.537
alpha1_hat	100	0	1.174	1.117	−1.140	0.994	4.438
alpha2_hat	100	0	0.489	0.121	0.227	0.496	0.754
alpha3_hat	100	0	1.002	0.118	0.800	0.995	1.399
gamma0_hat	100	0	1.610	0.638	−0.109	1.650	3.243
gamma1_hat	100	0	0.719	1.094	−2.132	0.852	3.085
gamma2_hat	100	0	0.934	0.101	0.679	0.927	1.175
gamma3_hat	100	0	0.937	0.098	0.719	0.927	1.223
theta_hat	100	0	0.025	0.198	−0.358	−0.010	0.611
theta_hat_t_stats	100	0	0.051	0.949	−1.910	−0.051	2.024
R2_demand	100	0	0.510	0.116	0.133	0.530	0.706
R2_supply	100	0	0.969	0.004	0.958	0.970	0.981

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.016	0.175	9.584	10.020	10.482
alpha1_hat	100	0	1.003	0.360	0.058	0.995	1.761
alpha2_hat	100	0	0.501	0.041	0.418	0.497	0.596
alpha3_hat	100	0	1.004	0.044	0.928	1.001	1.117
gamma0_hat	100	0	1.096	0.269	0.427	1.086	1.873
gamma1_hat	100	0	0.853	0.438	−0.121	0.881	1.988
gamma2_hat	100	0	0.988	0.042	0.869	0.986	1.111
gamma3_hat	100	0	0.985	0.043	0.870	0.985	1.112
theta_hat	100	0	0.062	0.084	−0.182	0.059	0.242
theta_hat_t_stats	100	0	0.720	0.982	−2.081	0.754	2.786
R2_demand	100	0	0.519	0.039	0.418	0.519	0.600
R2_supply	100	0	0.965	0.002	0.959	0.965	0.970

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.012	0.137	9.681	9.998	10.394
alpha1_hat	100	0	0.991	0.228	0.396	1.004	1.556
alpha2_hat	100	0	0.503	0.027	0.432	0.503	0.568
alpha3_hat	100	0	1.005	0.031	0.929	1.009	1.097
gamma0_hat	100	0	1.048	0.224	0.376	1.037	1.658
gamma1_hat	100	0	0.842	0.349	−0.032	0.874	1.637
gamma2_hat	100	0	0.995	0.035	0.918	0.995	1.118
gamma3_hat	100	0	0.994	0.034	0.925	0.989	1.088
theta_hat	100	0	0.069	0.063	−0.059	0.067	0.214
theta_hat_t_stats	100	0	1.171	1.054	−1.040	1.144	3.476
R2_demand	100	0	0.520	0.031	0.432	0.520	0.580
R2_supply	100	0	0.965	0.002	0.960	0.965	0.969

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.008	0.089	9.823	10.002	10.274
alpha1_hat	100	0	1.009	0.192	0.503	1.023	1.425
alpha2_hat	100	0	0.500	0.019	0.454	0.501	0.557
alpha3_hat	100	0	0.999	0.019	0.947	1.001	1.035
gamma0_hat	100	0	0.995	0.118	0.764	0.989	1.319
gamma1_hat	100	0	0.931	0.182	0.274	0.926	1.300
gamma2_hat	100	0	1.000	0.018	0.957	1.001	1.041
gamma3_hat	100	0	1.001	0.020	0.956	1.001	1.045
theta_hat	100	0	0.063	0.035	−0.025	0.067	0.164
theta_hat_t_stats	100	0	1.706	0.945	−0.710	1.807	4.355
R2_demand	100	0	0.519	0.021	0.463	0.522	0.557
R2_supply	100	0	0.964	0.001	0.962	0.964	0.967

\(\alpha_2 = 1.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.933	0.897	7.453	9.922	12.191
alpha1_hat	100	0	0.943	3.335	−7.741	1.125	8.999
alpha2_hat	100	0	0.990	0.372	−0.355	0.966	1.926
alpha3_hat	100	0	0.992	0.218	0.563	0.996	1.477
gamma0_hat	100	0	2.836	0.960	0.079	2.991	5.005
gamma1_hat	100	0	0.995	3.533	−11.836	0.886	9.696
gamma2_hat	100	0	0.809	0.159	0.481	0.789	1.310
gamma3_hat	100	0	0.812	0.169	0.502	0.791	1.429
theta_hat	100	0	−0.187	0.402	−1.684	−0.186	1.548
theta_hat_t_stats	100	0	−0.710	1.124	−4.112	−0.585	1.549
R2_demand	100	0	0.599	0.163	−0.154	0.641	0.834
R2_supply	100	0	0.973	0.007	0.946	0.974	0.985

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.938	0.640	8.767	9.912	11.649
alpha1_hat	100	0	1.277	2.296	−3.572	1.307	9.090
alpha2_hat	100	0	0.957	0.243	0.171	0.962	1.500
alpha3_hat	100	0	0.996	0.141	0.591	0.976	1.348
gamma0_hat	100	0	2.022	0.833	−0.589	2.029	4.037
gamma1_hat	100	0	0.160	2.450	−8.517	0.256	6.340
gamma2_hat	100	0	0.888	0.129	0.592	0.864	1.272
gamma3_hat	100	0	0.868	0.128	0.570	0.876	1.183
theta_hat	100	0	−0.005	0.260	−0.597	−0.025	0.806
theta_hat_t_stats	100	0	−0.130	1.020	−2.309	−0.104	2.600
R2_demand	100	0	0.562	0.128	0.062	0.583	0.757
R2_supply	100	0	0.968	0.007	0.935	0.969	0.984

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.007	0.499	8.849	9.898	12.162
alpha1_hat	100	0	1.156	1.481	−2.597	1.140	5.041
alpha2_hat	100	0	0.986	0.184	0.567	0.987	1.489
alpha3_hat	100	0	0.997	0.102	0.805	0.980	1.371
gamma0_hat	100	0	1.551	0.630	−0.070	1.570	3.106
gamma1_hat	100	0	0.604	1.457	−3.604	0.518	4.245
gamma2_hat	100	0	0.945	0.093	0.749	0.944	1.192
gamma3_hat	100	0	0.942	0.095	0.750	0.930	1.313
theta_hat	100	0	0.013	0.147	−0.369	0.009	0.470
theta_hat_t_stats	100	0	0.056	0.882	−1.815	0.049	2.129
R2_demand	100	0	0.570	0.128	−0.289	0.581	0.734
R2_supply	100	0	0.965	0.006	0.946	0.966	0.978

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.006	0.190	9.664	10.007	10.476
alpha1_hat	100	0	1.074	0.713	−0.916	1.075	3.064
alpha2_hat	100	0	0.994	0.084	0.760	0.989	1.234
alpha3_hat	100	0	0.998	0.048	0.896	0.995	1.125
gamma0_hat	100	0	1.123	0.281	0.222	1.122	1.709
gamma1_hat	100	0	0.666	0.653	−1.456	0.676	2.163
gamma2_hat	100	0	0.985	0.042	0.868	0.982	1.096
gamma3_hat	100	0	0.997	0.040	0.909	0.996	1.103
theta_hat	100	0	0.067	0.071	−0.130	0.067	0.317
theta_hat_t_stats	100	0	0.882	0.950	−1.893	0.893	3.821
R2_demand	100	0	0.570	0.032	0.490	0.574	0.662
R2_supply	100	0	0.961	0.003	0.954	0.961	0.968

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.010	0.126	9.731	9.995	10.335
alpha1_hat	100	0	1.019	0.463	0.015	1.021	2.032
alpha2_hat	100	0	1.000	0.053	0.850	1.000	1.129
alpha3_hat	100	0	1.003	0.031	0.938	1.005	1.062
gamma0_hat	100	0	1.020	0.215	0.530	1.013	1.578
gamma1_hat	100	0	0.769	0.515	−0.381	0.763	1.804
gamma2_hat	100	0	1.000	0.031	0.917	1.004	1.063
gamma3_hat	100	0	0.995	0.029	0.909	0.992	1.080
theta_hat	100	0	0.067	0.049	−0.042	0.063	0.183
theta_hat_t_stats	100	0	1.295	0.942	−0.858	1.253	3.598
R2_demand	100	0	0.571	0.024	0.493	0.572	0.614
R2_supply	100	0	0.960	0.002	0.953	0.960	0.966

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.012	0.085	9.768	10.013	10.200
alpha1_hat	100	0	1.054	0.308	0.219	1.050	1.716
alpha2_hat	100	0	0.997	0.033	0.930	0.993	1.075
alpha3_hat	100	0	1.003	0.020	0.959	1.002	1.049
gamma0_hat	100	0	1.010	0.144	0.637	1.012	1.378
gamma1_hat	100	0	0.878	0.322	−0.008	0.889	1.800
gamma2_hat	100	0	1.000	0.020	0.952	1.000	1.052
gamma3_hat	100	0	0.998	0.022	0.933	0.999	1.050
theta_hat	100	0	0.059	0.034	−0.026	0.059	0.142
theta_hat_t_stats	100	0	1.835	1.015	−0.792	1.819	4.317
R2_demand	100	0	0.567	0.017	0.533	0.569	0.607
R2_supply	100	0	0.960	0.002	0.956	0.960	0.963

\(\alpha_2 = 5.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.027	0.973	8.184	9.967	14.140
alpha1_hat	100	0	2.793	15.115	−34.879	2.222	36.412
alpha2_hat	100	0	4.848	1.764	1.841	4.817	9.933
alpha3_hat	100	0	1.004	0.222	0.481	0.970	1.743
gamma0_hat	100	0	3.089	1.022	0.466	3.230	5.484
gamma1_hat	100	0	1.026	13.342	−28.423	1.896	42.252
gamma2_hat	100	0	0.747	0.162	0.449	0.725	1.179
gamma3_hat	100	0	0.786	0.155	0.409	0.784	1.168
theta_hat	100	0	−0.190	0.297	−1.024	−0.181	0.618
theta_hat_t_stats	100	0	−0.794	1.045	−3.431	−0.842	1.642
R2_demand	100	0	0.591	0.189	−0.415	0.620	0.827
R2_supply	100	0	0.970	0.008	0.949	0.971	0.985

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.961	0.545	8.679	9.945	11.240
alpha1_hat	100	0	1.358	8.303	−18.125	1.695	18.536
alpha2_hat	100	0	4.939	0.965	2.676	4.963	7.482
alpha3_hat	100	0	0.994	0.134	0.628	0.996	1.392
gamma0_hat	100	0	2.042	0.695	0.286	2.186	3.414
gamma1_hat	100	0	−3.602	9.247	−31.453	−2.574	19.678
gamma2_hat	100	0	0.887	0.107	0.612	0.872	1.138
gamma3_hat	100	0	0.890	0.124	0.547	0.885	1.241
theta_hat	100	0	0.020	0.208	−0.449	0.004	0.722
theta_hat_t_stats	100	0	0.013	0.985	−2.259	0.024	2.894
R2_demand	100	0	0.622	0.105	0.291	0.640	0.816
R2_supply	100	0	0.965	0.008	0.945	0.966	0.981

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.967	0.396	9.046	9.941	10.802
alpha1_hat	100	0	0.952	7.211	−15.549	1.057	18.070
alpha2_hat	100	0	4.972	0.807	3.013	4.915	6.846
alpha3_hat	100	0	1.001	0.099	0.769	0.993	1.269
gamma0_hat	100	0	1.581	0.645	−0.328	1.640	2.854
gamma1_hat	100	0	−0.651	7.033	−18.899	−0.772	19.644
gamma2_hat	100	0	0.933	0.096	0.721	0.923	1.289
gamma3_hat	100	0	0.942	0.101	0.699	0.921	1.196
theta_hat	100	0	0.018	0.164	−0.444	0.009	0.444
theta_hat_t_stats	100	0	0.014	1.118	−3.397	0.077	2.303
R2_demand	100	0	0.620	0.068	0.439	0.633	0.746
R2_supply	100	0	0.960	0.007	0.937	0.962	0.973

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.021	0.196	9.574	9.984	10.626
alpha1_hat	100	0	1.292	2.799	−5.567	0.953	9.036
alpha2_hat	100	0	4.988	0.341	4.140	4.967	5.810
alpha3_hat	100	0	1.001	0.047	0.903	1.002	1.120
gamma0_hat	100	0	1.091	0.296	0.172	1.088	1.665
gamma1_hat	100	0	−0.098	2.863	−5.344	0.146	6.711
gamma2_hat	100	0	0.989	0.043	0.897	0.989	1.111
gamma3_hat	100	0	0.994	0.046	0.875	0.990	1.097
theta_hat	100	0	0.061	0.067	−0.090	0.054	0.199
theta_hat_t_stats	100	0	0.909	1.014	−1.544	0.868	2.982
R2_demand	100	0	0.617	0.036	0.502	0.619	0.691
R2_supply	100	0	0.956	0.003	0.947	0.956	0.962

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.003	0.139	9.664	9.999	10.391
alpha1_hat	100	0	0.892	1.788	−4.114	0.834	4.986
alpha2_hat	100	0	5.011	0.207	4.459	5.035	5.508
alpha3_hat	100	0	0.999	0.029	0.933	0.997	1.060
gamma0_hat	100	0	1.055	0.195	0.551	1.059	1.599
gamma1_hat	100	0	0.116	2.033	−6.430	0.113	5.167
gamma2_hat	100	0	0.995	0.028	0.920	0.996	1.067
gamma3_hat	100	0	0.994	0.032	0.922	0.992	1.063
theta_hat	100	0	0.060	0.045	−0.053	0.063	0.207
theta_hat_t_stats	100	0	1.312	0.967	−1.225	1.387	4.180
R2_demand	100	0	0.619	0.023	0.550	0.624	0.662
R2_supply	100	0	0.955	0.002	0.948	0.955	0.961

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.000	0.082	9.776	9.995	10.227
alpha1_hat	100	0	0.978	1.209	−2.241	1.031	4.140
alpha2_hat	100	0	5.003	0.142	4.679	4.974	5.388
alpha3_hat	100	0	1.001	0.019	0.959	1.000	1.047
gamma0_hat	100	0	1.019	0.119	0.737	1.012	1.293
gamma1_hat	100	0	0.414	1.253	−2.735	0.604	3.096
gamma2_hat	100	0	0.999	0.018	0.954	0.998	1.047
gamma3_hat	100	0	0.999	0.019	0.926	1.001	1.047
theta_hat	100	0	0.059	0.025	0.006	0.056	0.122
theta_hat_t_stats	100	0	2.057	0.841	0.212	1.953	4.169
R2_demand	100	0	0.620	0.014	0.587	0.621	0.653
R2_supply	100	0	0.955	0.001	0.950	0.955	0.958

\(\alpha_2 = 20.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.078	1.156	7.657	10.040	17.632
alpha1_hat	100	0	2.394	47.415	−116.140	1.858	116.686
alpha2_hat	100	0	20.067	5.963	8.920	19.537	49.105
alpha3_hat	100	0	1.028	0.243	0.532	0.999	2.502
gamma0_hat	100	0	2.937	0.912	−0.206	2.934	5.571
gamma1_hat	100	0	4.394	45.937	−85.423	5.066	177.419
gamma2_hat	100	0	0.784	0.160	0.394	0.800	1.104
gamma3_hat	100	0	0.779	0.164	0.482	0.773	1.371
theta_hat	100	0	−0.197	0.276	−1.358	−0.161	0.495
theta_hat_t_stats	100	0	−0.785	0.981	−3.183	−0.665	1.624
R2_demand	100	0	0.564	0.537	−4.527	0.655	0.827
R2_supply	100	0	0.969	0.009	0.917	0.969	0.983

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.000	0.682	8.803	9.929	12.743
alpha1_hat	100	0	2.544	33.319	−74.863	0.205	79.604
alpha2_hat	100	0	19.850	3.830	11.814	20.057	30.398
alpha3_hat	100	0	0.992	0.157	0.692	0.984	1.611
gamma0_hat	100	0	2.125	0.706	−0.080	2.160	3.545
gamma1_hat	100	0	−8.277	35.057	−128.621	−5.857	72.619
gamma2_hat	100	0	0.886	0.116	0.600	0.890	1.161
gamma3_hat	100	0	0.874	0.114	0.567	0.883	1.121
theta_hat	100	0	−0.038	0.203	−0.433	−0.050	0.611
theta_hat_t_stats	100	0	−0.307	1.123	−3.312	−0.284	2.416
R2_demand	100	0	0.618	0.129	−0.022	0.636	0.788
R2_supply	100	0	0.964	0.007	0.940	0.965	0.977

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.994	0.371	9.163	10.035	11.065
alpha1_hat	100	0	0.532	21.853	−67.392	−0.577	48.025
alpha2_hat	100	0	20.039	2.642	13.664	20.145	27.673
alpha3_hat	100	0	0.991	0.103	0.703	1.002	1.231
gamma0_hat	100	0	1.579	0.648	−0.396	1.620	2.777
gamma1_hat	100	0	−3.567	19.372	−65.107	−1.989	47.302
gamma2_hat	100	0	0.943	0.095	0.730	0.938	1.191
gamma3_hat	100	0	0.938	0.093	0.744	0.933	1.336
theta_hat	100	0	0.003	0.132	−0.288	−0.010	0.363
theta_hat_t_stats	100	0	−0.048	0.923	−2.355	−0.068	2.451
R2_demand	100	0	0.633	0.073	0.391	0.644	0.773
R2_supply	100	0	0.959	0.006	0.940	0.959	0.972

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.019	0.174	9.616	10.026	10.367
alpha1_hat	100	0	−0.831	10.322	−28.642	−1.953	26.857
alpha2_hat	100	0	20.251	1.177	16.694	20.211	23.084
alpha3_hat	100	0	1.006	0.041	0.912	1.012	1.103
gamma0_hat	100	0	1.037	0.298	0.296	1.033	1.940
gamma1_hat	100	0	−5.669	10.546	−31.365	−6.112	20.330
gamma2_hat	100	0	1.000	0.043	0.881	0.999	1.139
gamma3_hat	100	0	0.993	0.045	0.857	0.993	1.124
theta_hat	100	0	0.077	0.062	−0.065	0.078	0.211
theta_hat_t_stats	100	0	1.190	0.940	−1.156	1.217	3.214
R2_demand	100	0	0.634	0.028	0.545	0.635	0.696
R2_supply	100	0	0.954	0.004	0.941	0.954	0.962

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.999	0.137	9.610	10.001	10.327
alpha1_hat	100	0	1.356	8.204	−15.540	0.259	21.595
alpha2_hat	100	0	19.974	0.969	18.050	19.986	22.431
alpha3_hat	100	0	1.004	0.032	0.889	1.004	1.073
gamma0_hat	100	0	1.038	0.191	0.468	1.049	1.391
gamma1_hat	100	0	−1.267	6.793	−18.113	−1.247	16.619
gamma2_hat	100	0	0.997	0.031	0.928	0.997	1.087
gamma3_hat	100	0	0.994	0.032	0.911	0.991	1.074
theta_hat	100	0	0.057	0.041	−0.029	0.056	0.150
theta_hat_t_stats	100	0	1.250	0.890	−0.731	1.258	3.279
R2_demand	100	0	0.630	0.022	0.580	0.629	0.688
R2_supply	100	0	0.954	0.003	0.945	0.954	0.959

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.991	0.076	9.851	9.981	10.176
alpha1_hat	100	0	0.919	4.200	−9.902	0.690	14.379
alpha2_hat	100	0	19.977	0.462	18.729	20.022	21.168
alpha3_hat	100	0	1.000	0.017	0.952	1.000	1.040
gamma0_hat	100	0	1.015	0.132	0.642	1.024	1.327
gamma1_hat	100	0	−0.318	4.568	−11.722	−0.385	11.991
gamma2_hat	100	0	0.999	0.021	0.946	0.996	1.060
gamma3_hat	100	0	0.999	0.020	0.952	1.001	1.050
theta_hat	100	0	0.055	0.026	−0.030	0.055	0.119
theta_hat_t_stats	100	0	1.931	0.913	−1.128	1.958	4.174
R2_demand	100	0	0.631	0.013	0.602	0.633	0.659
R2_supply	100	0	0.953	0.001	0.950	0.953	0.957

\(\theta = 0.1\)

\(\alpha_2 = 0.1\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.922	1.004	7.786	9.863	14.467
alpha1_hat	100	0	0.980	0.866	−0.802	0.867	3.118
alpha2_hat	100	0	0.097	0.084	−0.101	0.096	0.362
alpha3_hat	100	0	0.993	0.247	0.475	0.952	2.143
gamma0_hat	100	0	2.892	0.988	−0.253	2.980	5.471
gamma1_hat	100	0	0.010	7.095	−41.040	0.664	16.645
gamma2_hat	100	0	0.784	0.170	0.269	0.783	1.253
gamma3_hat	100	0	0.791	0.147	0.345	0.790	1.181
theta_hat	100	0	0.286	3.885	−6.646	−0.111	20.789
theta_hat_t_stats	100	0	−0.158	1.073	−2.478	−0.216	3.201
R2_demand	100	0	0.313	0.320	−1.342	0.399	0.705
R2_supply	100	0	0.983	0.004	0.974	0.984	0.991

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.982	0.793	8.536	9.913	14.488
alpha1_hat	100	0	0.983	0.706	−0.476	0.892	4.420
alpha2_hat	100	0	0.101	0.061	−0.055	0.101	0.364
alpha3_hat	100	0	0.998	0.183	0.695	0.974	2.060
gamma0_hat	100	0	2.222	0.666	−0.070	2.137	3.709
gamma1_hat	100	0	1.256	6.325	−18.097	0.790	50.485
gamma2_hat	100	0	0.861	0.106	0.613	0.867	1.254
gamma3_hat	100	0	0.866	0.130	0.528	0.856	1.176
theta_hat	100	0	−0.051	2.299	−12.842	−0.016	10.421
theta_hat_t_stats	100	0	0.041	1.041	−2.186	−0.041	2.428
R2_demand	100	0	0.279	0.311	−2.128	0.345	0.582
R2_supply	100	0	0.981	0.003	0.971	0.981	0.989

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.017	0.514	8.751	9.988	11.461
alpha1_hat	100	0	1.064	0.383	0.235	1.066	1.977
alpha2_hat	100	0	0.094	0.040	0.005	0.091	0.220
alpha3_hat	100	0	1.007	0.101	0.823	0.997	1.310
gamma0_hat	100	0	1.586	0.694	−0.451	1.564	3.133
gamma1_hat	100	0	0.717	1.565	−10.581	0.950	5.447
gamma2_hat	100	0	0.933	0.102	0.720	0.929	1.198
gamma3_hat	100	0	0.944	0.105	0.728	0.937	1.271
theta_hat	100	0	0.133	0.789	−2.257	0.079	5.603
theta_hat_t_stats	100	0	0.159	1.108	−2.455	0.209	2.976
R2_demand	100	0	0.310	0.134	−0.144	0.327	0.574
R2_supply	100	0	0.978	0.004	0.967	0.979	0.985

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.008	0.185	9.641	10.009	10.470
alpha1_hat	100	0	0.987	0.168	0.606	0.985	1.521
alpha2_hat	100	0	0.102	0.016	0.055	0.102	0.131
alpha3_hat	100	0	0.998	0.046	0.873	0.998	1.120
gamma0_hat	100	0	1.132	0.316	0.412	1.129	1.968
gamma1_hat	100	0	0.954	0.340	0.024	0.950	1.740
gamma2_hat	100	0	0.984	0.043	0.884	0.984	1.075
gamma3_hat	100	0	0.987	0.051	0.862	0.988	1.087
theta_hat	100	0	0.100	0.181	−0.285	0.090	0.626
theta_hat_t_stats	100	0	0.566	1.076	−1.891	0.563	3.805
R2_demand	100	0	0.313	0.051	0.186	0.323	0.403
R2_supply	100	0	0.976	0.002	0.971	0.976	0.980

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.998	0.150	9.650	10.002	10.424
alpha1_hat	100	0	0.987	0.123	0.569	0.993	1.312
alpha2_hat	100	0	0.101	0.012	0.072	0.101	0.125
alpha3_hat	100	0	1.001	0.036	0.910	1.001	1.110
gamma0_hat	100	0	1.033	0.220	0.418	1.038	1.522
gamma1_hat	100	0	0.914	0.255	0.107	0.922	1.475
gamma2_hat	100	0	0.997	0.033	0.918	0.992	1.096
gamma3_hat	100	0	0.997	0.032	0.916	1.000	1.074
theta_hat	100	0	0.138	0.131	−0.141	0.117	0.529
theta_hat_t_stats	100	0	1.113	1.029	−1.244	1.078	3.978
R2_demand	100	0	0.312	0.040	0.198	0.314	0.415
R2_supply	100	0	0.976	0.001	0.973	0.976	0.979

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.007	0.082	9.812	10.004	10.206
alpha1_hat	100	0	0.989	0.081	0.798	0.978	1.193
alpha2_hat	100	0	0.102	0.008	0.084	0.101	0.120
alpha3_hat	100	0	1.002	0.020	0.962	1.003	1.054
gamma0_hat	100	0	0.992	0.133	0.568	0.997	1.294
gamma1_hat	100	0	0.959	0.137	0.520	0.975	1.405
gamma2_hat	100	0	1.002	0.020	0.947	1.000	1.050
gamma3_hat	100	0	1.000	0.019	0.944	1.000	1.049
theta_hat	100	0	0.121	0.070	−0.075	0.118	0.337
theta_hat_t_stats	100	0	1.611	0.918	−0.885	1.539	4.520
R2_demand	100	0	0.312	0.026	0.243	0.314	0.360
R2_supply	100	0	0.975	0.001	0.973	0.975	0.978

\(\alpha_2 = 0.5\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.978	1.100	7.673	9.744	14.551
alpha1_hat	100	0	1.068	2.043	−3.604	1.104	9.409
alpha2_hat	100	0	0.491	0.222	−0.065	0.470	1.043
alpha3_hat	100	0	0.979	0.220	0.433	0.949	1.703
gamma0_hat	100	0	2.983	1.028	0.200	3.098	5.262
gamma1_hat	100	0	18.483	181.127	−14.730	0.925	1811.410
gamma2_hat	100	0	0.782	0.169	0.354	0.770	1.271
gamma3_hat	100	0	0.781	0.167	0.356	0.768	1.186
theta_hat	100	0	−4.103	40.295	−402.988	−0.172	2.947
theta_hat_t_stats	100	0	−0.392	1.050	−2.365	−0.497	2.655
R2_demand	100	0	0.441	0.308	−1.486	0.501	0.798
R2_supply	100	0	0.978	0.005	0.961	0.979	0.989

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.938	0.726	8.691	9.844	12.232
alpha1_hat	100	0	1.088	1.283	−2.326	1.066	5.789
alpha2_hat	100	0	0.484	0.140	0.028	0.491	0.981
alpha3_hat	100	0	0.991	0.157	0.605	0.962	1.598
gamma0_hat	100	0	2.236	0.774	0.428	2.349	4.294
gamma1_hat	100	0	0.152	4.327	−40.126	0.575	4.938
gamma2_hat	100	0	0.854	0.130	0.565	0.847	1.316
gamma3_hat	100	0	0.855	0.125	0.456	0.853	1.171
theta_hat	100	0	0.091	0.897	−0.713	0.007	8.467
theta_hat_t_stats	100	0	−0.073	1.051	−3.166	0.016	2.879
R2_demand	100	0	0.469	0.192	−0.342	0.511	0.774
R2_supply	100	0	0.974	0.005	0.959	0.975	0.984

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.041	0.475	9.076	10.000	11.728
alpha1_hat	100	0	1.054	1.037	−1.468	0.926	3.057
alpha2_hat	100	0	0.500	0.112	0.204	0.497	0.780
alpha3_hat	100	0	1.010	0.110	0.765	1.016	1.246
gamma0_hat	100	0	1.570	0.703	−0.253	1.680	2.958
gamma1_hat	100	0	0.773	1.050	−1.318	0.770	3.983
gamma2_hat	100	0	0.941	0.108	0.737	0.935	1.208
gamma3_hat	100	0	0.918	0.096	0.715	0.896	1.153
theta_hat	100	0	0.054	0.208	−0.436	0.053	0.571
theta_hat_t_stats	100	0	0.216	1.089	−3.558	0.213	2.777
R2_demand	100	0	0.477	0.126	−0.315	0.500	0.643
R2_supply	100	0	0.970	0.005	0.954	0.971	0.981

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.042	0.185	9.652	10.034	10.520
alpha1_hat	100	0	0.969	0.399	−0.250	0.997	2.022
alpha2_hat	100	0	0.509	0.044	0.410	0.505	0.621
alpha3_hat	100	0	1.014	0.047	0.912	1.011	1.141
gamma0_hat	100	0	1.124	0.248	0.508	1.118	1.689
gamma1_hat	100	0	0.760	0.416	−0.294	0.751	1.676
gamma2_hat	100	0	0.984	0.041	0.905	0.982	1.097
gamma3_hat	100	0	0.990	0.040	0.911	0.989	1.108
theta_hat	100	0	0.123	0.073	−0.018	0.117	0.305
theta_hat_t_stats	100	0	1.452	0.844	−0.245	1.451	3.473
R2_demand	100	0	0.480	0.045	0.378	0.482	0.572
R2_supply	100	0	0.967	0.002	0.961	0.968	0.972

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.972	0.131	9.681	9.966	10.273
alpha1_hat	100	0	0.966	0.276	−0.048	0.946	1.588
alpha2_hat	100	0	0.500	0.029	0.443	0.499	0.601
alpha3_hat	100	0	0.997	0.031	0.923	0.993	1.096
gamma0_hat	100	0	1.046	0.206	0.419	1.059	1.545
gamma1_hat	100	0	0.840	0.352	−0.008	0.817	1.632
gamma2_hat	100	0	0.995	0.028	0.929	0.992	1.079
gamma3_hat	100	0	0.996	0.030	0.936	0.994	1.081
theta_hat	100	0	0.121	0.063	−0.009	0.113	0.297
theta_hat_t_stats	100	0	2.002	1.009	−0.139	1.904	4.502
R2_demand	100	0	0.494	0.031	0.424	0.492	0.594
R2_supply	100	0	0.967	0.002	0.960	0.967	0.971

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.005	0.087	9.848	9.996	10.264
alpha1_hat	100	0	1.028	0.182	0.705	1.010	1.504
alpha2_hat	100	0	0.498	0.019	0.447	0.501	0.534
alpha3_hat	100	0	0.999	0.019	0.961	0.995	1.057
gamma0_hat	100	0	1.041	0.121	0.703	1.046	1.313
gamma1_hat	100	0	0.920	0.223	0.353	0.907	1.352
gamma2_hat	100	0	0.995	0.019	0.955	0.996	1.054
gamma3_hat	100	0	0.996	0.019	0.950	0.996	1.046
theta_hat	100	0	0.108	0.039	0.039	0.107	0.214
theta_hat_t_stats	100	0	2.830	0.967	1.087	2.866	5.420
R2_demand	100	0	0.490	0.020	0.428	0.492	0.528
R2_supply	100	0	0.967	0.001	0.964	0.966	0.970

\(\alpha_2 = 1.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.038	0.939	8.563	9.859	13.464
alpha1_hat	100	0	1.139	3.316	−7.905	0.999	9.244
alpha2_hat	100	0	0.998	0.364	0.259	0.969	1.958
alpha3_hat	100	0	1.000	0.203	0.591	0.988	1.603
gamma0_hat	100	0	2.814	0.928	−0.982	3.001	4.362
gamma1_hat	100	0	0.947	4.313	−13.915	1.424	22.212
gamma2_hat	100	0	0.799	0.154	0.501	0.785	1.293
gamma3_hat	100	0	0.802	0.173	0.265	0.811	1.372
theta_hat	100	0	−0.121	0.424	−1.644	−0.176	1.541
theta_hat_t_stats	100	0	−0.534	1.010	−3.560	−0.631	2.053
R2_demand	100	0	0.501	0.210	−0.175	0.550	0.766
R2_supply	100	0	0.975	0.006	0.949	0.976	0.985

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.998	0.699	8.589	10.008	12.681
alpha1_hat	100	0	0.966	2.437	−7.025	0.897	6.588
alpha2_hat	100	0	1.004	0.283	0.358	1.009	1.796
alpha3_hat	100	0	0.992	0.162	0.666	0.982	1.479
gamma0_hat	100	0	2.072	0.810	0.331	2.160	3.910
gamma1_hat	100	0	0.328	3.135	−11.179	0.558	7.827
gamma2_hat	100	0	0.884	0.132	0.517	0.882	1.157
gamma3_hat	100	0	0.874	0.112	0.585	0.884	1.124
theta_hat	100	0	0.020	0.320	−0.615	−0.002	1.418
theta_hat_t_stats	100	0	−0.056	1.088	−2.581	−0.011	2.371
R2_demand	100	0	0.535	0.142	0.009	0.559	0.772
R2_supply	100	0	0.970	0.006	0.955	0.971	0.982

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.052	0.470	9.294	9.975	11.816
alpha1_hat	100	0	0.985	1.597	−3.600	1.158	5.063
alpha2_hat	100	0	1.013	0.187	0.547	0.993	1.675
alpha3_hat	100	0	1.009	0.109	0.786	1.004	1.354
gamma0_hat	100	0	1.592	0.519	0.212	1.646	2.863
gamma1_hat	100	0	0.510	1.737	−4.169	0.554	4.488
gamma2_hat	100	0	0.936	0.085	0.757	0.926	1.178
gamma3_hat	100	0	0.932	0.083	0.747	0.930	1.180
theta_hat	100	0	0.064	0.169	−0.331	0.058	0.662
theta_hat_t_stats	100	0	0.352	0.968	−1.713	0.318	2.701
R2_demand	100	0	0.529	0.112	−0.065	0.552	0.714
R2_supply	100	0	0.967	0.005	0.947	0.967	0.978

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.016	0.198	9.512	9.995	10.631
alpha1_hat	100	0	1.035	0.685	−1.053	1.009	3.025
alpha2_hat	100	0	0.999	0.082	0.797	1.003	1.248
alpha3_hat	100	0	0.997	0.049	0.896	0.992	1.156
gamma0_hat	100	0	1.062	0.341	0.218	1.053	1.947
gamma1_hat	100	0	0.785	0.791	−0.974	0.730	2.507
gamma2_hat	100	0	0.993	0.050	0.868	0.998	1.106
gamma3_hat	100	0	0.986	0.048	0.858	0.984	1.134
theta_hat	100	0	0.113	0.083	−0.092	0.118	0.290
theta_hat_t_stats	100	0	1.436	1.048	−1.267	1.549	3.372
R2_demand	100	0	0.529	0.041	0.420	0.531	0.624
R2_supply	100	0	0.963	0.003	0.955	0.963	0.970

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.994	0.127	9.689	9.981	10.334
alpha1_hat	100	0	1.076	0.462	0.143	1.053	2.293
alpha2_hat	100	0	0.991	0.046	0.883	0.987	1.095
alpha3_hat	100	0	1.002	0.031	0.902	1.001	1.075
gamma0_hat	100	0	1.043	0.205	0.528	1.036	1.514
gamma1_hat	100	0	0.777	0.491	−0.914	0.806	1.927
gamma2_hat	100	0	0.996	0.029	0.922	0.998	1.077
gamma3_hat	100	0	0.993	0.033	0.920	0.992	1.066
theta_hat	100	0	0.114	0.051	−0.025	0.108	0.288
theta_hat_t_stats	100	0	2.105	0.905	−0.488	2.012	4.869
R2_demand	100	0	0.540	0.023	0.480	0.543	0.612
R2_supply	100	0	0.963	0.002	0.957	0.963	0.968

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.002	0.094	9.754	10.008	10.219
alpha1_hat	100	0	0.994	0.269	0.298	0.992	1.531
alpha2_hat	100	0	1.001	0.032	0.908	0.999	1.076
alpha3_hat	100	0	1.000	0.021	0.955	0.997	1.054
gamma0_hat	100	0	1.019	0.116	0.747	1.019	1.305
gamma1_hat	100	0	0.899	0.267	0.327	0.893	1.472
gamma2_hat	100	0	0.997	0.019	0.951	0.997	1.038
gamma3_hat	100	0	0.995	0.020	0.948	0.999	1.036
theta_hat	100	0	0.108	0.027	0.050	0.107	0.167
theta_hat_t_stats	100	0	3.209	0.770	1.479	3.228	4.868
R2_demand	100	0	0.539	0.018	0.494	0.538	0.586
R2_supply	100	0	0.963	0.001	0.960	0.963	0.966

\(\alpha_2 = 5.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.972	0.721	8.034	9.826	12.227
alpha1_hat	100	0	0.732	12.626	−30.189	1.279	31.383
alpha2_hat	100	0	5.012	1.345	2.416	4.866	8.509
alpha3_hat	100	0	1.007	0.213	0.575	0.995	1.646
gamma0_hat	100	0	2.909	0.974	0.794	2.946	5.611
gamma1_hat	100	0	−1.424	12.045	−32.763	−0.614	22.017
gamma2_hat	100	0	0.785	0.162	0.493	0.768	1.260
gamma3_hat	100	0	0.788	0.164	0.437	0.793	1.217
theta_hat	100	0	−0.100	0.258	−0.641	−0.096	0.476
theta_hat_t_stats	100	0	−0.439	1.010	−3.013	−0.338	1.789
R2_demand	100	0	0.563	0.203	−0.275	0.602	0.819
R2_supply	100	0	0.973	0.006	0.954	0.974	0.985

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.938	0.567	8.736	9.990	11.303
alpha1_hat	100	0	1.609	10.753	−29.624	1.950	38.203
alpha2_hat	100	0	4.877	1.207	1.285	4.847	9.029
alpha3_hat	100	0	1.003	0.133	0.770	0.995	1.363
gamma0_hat	100	0	2.034	0.741	−0.306	2.138	4.336
gamma1_hat	100	0	−3.129	10.206	−54.722	−2.579	20.806
gamma2_hat	100	0	0.888	0.116	0.589	0.876	1.292
gamma3_hat	100	0	0.898	0.132	0.522	0.906	1.229
theta_hat	100	0	0.053	0.235	−0.380	0.017	1.222
theta_hat_t_stats	100	0	0.125	0.886	−2.836	0.083	2.072
R2_demand	100	0	0.591	0.112	0.243	0.613	0.799
R2_supply	100	0	0.967	0.006	0.943	0.968	0.979

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.030	0.447	8.912	9.959	11.050
alpha1_hat	100	0	0.800	6.976	−16.810	0.746	18.238
alpha2_hat	100	0	5.048	0.844	3.433	5.046	7.572
alpha3_hat	100	0	1.011	0.106	0.760	1.009	1.282
gamma0_hat	100	0	1.493	0.570	0.297	1.536	2.739
gamma1_hat	100	0	−0.586	7.242	−20.630	−0.893	19.034
gamma2_hat	100	0	0.949	0.090	0.760	0.949	1.171
gamma3_hat	100	0	0.949	0.094	0.754	0.946	1.187
theta_hat	100	0	0.070	0.160	−0.330	0.063	0.537
theta_hat_t_stats	100	0	0.416	1.007	−2.639	0.481	2.904
R2_demand	100	0	0.576	0.088	0.266	0.592	0.736
R2_supply	100	0	0.963	0.005	0.948	0.964	0.975

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.000	0.183	9.653	9.977	10.385
alpha1_hat	100	0	1.291	2.956	−5.136	1.479	7.205
alpha2_hat	100	0	4.973	0.360	4.186	4.986	5.969
alpha3_hat	100	0	1.008	0.041	0.921	1.010	1.142
gamma0_hat	100	0	1.016	0.290	0.230	1.004	1.657
gamma1_hat	100	0	−0.149	2.827	−6.893	0.005	5.369
gamma2_hat	100	0	0.999	0.045	0.880	0.997	1.096
gamma3_hat	100	0	0.999	0.040	0.915	1.002	1.102
theta_hat	100	0	0.121	0.067	−0.055	0.121	0.283
theta_hat_t_stats	100	0	1.722	0.900	−0.935	1.822	3.725
R2_demand	100	0	0.588	0.034	0.509	0.589	0.674
R2_supply	100	0	0.959	0.003	0.945	0.959	0.966

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.985	0.133	9.706	9.966	10.504
alpha1_hat	100	0	0.858	2.075	−4.874	0.888	6.281
alpha2_hat	100	0	4.998	0.252	4.389	4.956	5.689
alpha3_hat	100	0	0.998	0.028	0.949	0.999	1.086
gamma0_hat	100	0	1.034	0.208	0.437	1.029	1.627
gamma1_hat	100	0	−0.012	2.086	−4.701	0.026	5.679
gamma2_hat	100	0	0.996	0.030	0.925	0.998	1.073
gamma3_hat	100	0	0.999	0.037	0.908	0.999	1.088
theta_hat	100	0	0.116	0.052	−0.014	0.120	0.232
theta_hat_t_stats	100	0	2.405	1.037	−0.320	2.525	4.656
R2_demand	100	0	0.589	0.025	0.499	0.591	0.629
R2_supply	100	0	0.959	0.002	0.953	0.959	0.964

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.999	0.086	9.818	9.988	10.300
alpha1_hat	100	0	0.973	1.200	−1.703	0.997	3.804
alpha2_hat	100	0	5.003	0.145	4.683	5.007	5.338
alpha3_hat	100	0	1.001	0.020	0.954	0.999	1.047
gamma0_hat	100	0	1.020	0.132	0.763	1.016	1.308
gamma1_hat	100	0	0.739	1.314	−1.709	0.774	3.626
gamma2_hat	100	0	0.998	0.020	0.956	0.996	1.045
gamma3_hat	100	0	0.997	0.018	0.947	0.996	1.046
theta_hat	100	0	0.103	0.029	0.037	0.105	0.173
theta_hat_t_stats	100	0	3.417	0.927	1.246	3.520	5.639
R2_demand	100	0	0.586	0.019	0.531	0.586	0.626
R2_supply	100	0	0.958	0.001	0.955	0.958	0.962

\(\alpha_2 = 20.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.009	0.849	8.005	9.985	12.852
alpha1_hat	100	0	−1.334	57.303	−166.001	−4.268	170.300
alpha2_hat	100	0	20.221	6.912	0.669	19.854	41.702
alpha3_hat	100	0	0.983	0.197	0.505	0.978	1.448
gamma0_hat	100	0	2.863	0.964	−0.398	2.959	5.120
gamma1_hat	100	0	−31.207	183.952	−1779.277	−7.554	101.065
gamma2_hat	100	0	0.805	0.160	0.321	0.810	1.230
gamma3_hat	100	0	0.803	0.153	0.492	0.802	1.149
theta_hat	100	0	0.042	1.043	−0.859	−0.097	9.877
theta_hat_t_stats	100	0	−0.312	1.056	−2.501	−0.412	2.327
R2_demand	100	0	0.585	0.161	−0.060	0.619	0.858
R2_supply	100	0	0.972	0.007	0.943	0.973	0.984

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.136	0.644	8.713	10.140	11.647
alpha1_hat	100	0	−0.463	41.128	−102.521	0.213	130.323
alpha2_hat	100	0	20.640	4.822	8.791	20.220	31.189
alpha3_hat	100	0	1.009	0.145	0.699	1.004	1.313
gamma0_hat	100	0	1.947	0.803	−0.751	1.899	3.948
gamma1_hat	100	0	−4.245	36.973	−90.244	0.119	85.974
gamma2_hat	100	0	0.901	0.135	0.580	0.904	1.350
gamma3_hat	100	0	0.884	0.128	0.611	0.886	1.224
theta_hat	100	0	0.002	0.205	−0.377	−0.028	0.484
theta_hat_t_stats	100	0	−0.053	1.046	−2.429	−0.151	2.352
R2_demand	100	0	0.563	0.146	0.035	0.586	0.793
R2_supply	100	0	0.967	0.006	0.944	0.967	0.979

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.963	0.437	9.013	9.902	11.204
alpha1_hat	100	0	−3.256	26.239	−73.104	−0.447	61.611
alpha2_hat	100	0	20.285	3.231	13.759	20.306	30.019
alpha3_hat	100	0	0.998	0.111	0.765	0.996	1.329
gamma0_hat	100	0	1.487	0.567	0.439	1.521	2.653
gamma1_hat	100	0	−6.876	22.782	−87.167	−7.047	73.582
gamma2_hat	100	0	0.947	0.085	0.730	0.939	1.122
gamma3_hat	100	0	0.953	0.095	0.738	0.954	1.203
theta_hat	100	0	0.082	0.137	−0.348	0.078	0.508
theta_hat_t_stats	100	0	0.512	0.917	−2.380	0.554	2.722
R2_demand	100	0	0.594	0.078	0.364	0.594	0.772
R2_supply	100	0	0.962	0.005	0.946	0.962	0.974

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.995	0.207	9.460	10.015	10.476
alpha1_hat	100	0	0.251	10.457	−23.319	2.316	21.523
alpha2_hat	100	0	20.076	1.288	16.737	19.948	23.231
alpha3_hat	100	0	0.999	0.049	0.851	0.997	1.119
gamma0_hat	100	0	1.006	0.337	0.285	0.979	1.771
gamma1_hat	100	0	−2.841	10.198	−23.601	−2.792	27.481
gamma2_hat	100	0	1.002	0.048	0.893	0.993	1.112
gamma3_hat	100	0	1.004	0.041	0.899	1.005	1.118
theta_hat	100	0	0.117	0.062	−0.024	0.125	0.238
theta_hat_t_stats	100	0	1.724	0.878	−0.350	1.841	3.418
R2_demand	100	0	0.595	0.039	0.461	0.595	0.667
R2_supply	100	0	0.958	0.003	0.948	0.957	0.966

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.992	0.142	9.640	9.988	10.326
alpha1_hat	100	0	0.453	8.219	−19.675	0.204	15.929
alpha2_hat	100	0	20.017	0.956	17.485	20.057	22.606
alpha3_hat	100	0	0.995	0.034	0.903	0.992	1.085
gamma0_hat	100	0	1.049	0.210	0.591	1.050	1.481
gamma1_hat	100	0	−2.200	8.785	−25.017	−2.620	21.102
gamma2_hat	100	0	0.990	0.029	0.921	0.991	1.064
gamma3_hat	100	0	0.999	0.030	0.934	0.998	1.080
theta_hat	100	0	0.113	0.051	−0.031	0.111	0.225
theta_hat_t_stats	100	0	2.390	0.997	−0.682	2.398	4.436
R2_demand	100	0	0.597	0.026	0.518	0.600	0.642
R2_supply	100	0	0.958	0.002	0.952	0.958	0.963

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.003	0.091	9.785	9.992	10.190
alpha1_hat	100	0	0.643	4.690	−10.223	0.769	11.030
alpha2_hat	100	0	20.054	0.586	18.926	20.051	21.517
alpha3_hat	100	0	1.001	0.020	0.945	1.003	1.045
gamma0_hat	100	0	1.027	0.147	0.690	1.029	1.374
gamma1_hat	100	0	0.749	4.711	−9.806	0.376	17.872
gamma2_hat	100	0	0.995	0.022	0.953	0.996	1.055
gamma3_hat	100	0	0.999	0.021	0.951	0.998	1.058
theta_hat	100	0	0.099	0.029	0.012	0.103	0.161
theta_hat_t_stats	100	0	3.371	0.954	0.398	3.474	5.403
R2_demand	100	0	0.594	0.017	0.556	0.596	0.628
R2_supply	100	0	0.957	0.002	0.953	0.957	0.960

\(\theta = 0.2\)

\(\alpha_2 = 0.1\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.075	1.011	7.398	10.061	13.437
alpha1_hat	100	0	1.091	0.872	−0.569	1.004	5.993
alpha2_hat	100	0	0.095	0.088	−0.270	0.097	0.283
alpha3_hat	100	0	1.004	0.238	0.588	0.981	1.694
gamma0_hat	100	0	2.879	1.120	−0.875	3.002	5.823
gamma1_hat	100	0	2.126	15.596	−56.115	0.641	102.696
gamma2_hat	100	0	0.795	0.173	0.388	0.767	1.180
gamma3_hat	100	0	0.772	0.165	0.372	0.770	1.143
theta_hat	100	0	−0.849	8.934	−66.411	−0.067	30.588
theta_hat_t_stats	100	0	0.000	1.048	−2.132	−0.034	2.463
R2_demand	100	0	0.229	0.389	−1.627	0.339	0.609
R2_supply	100	0	0.984	0.004	0.974	0.984	0.992

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.926	0.661	8.653	9.862	11.727
alpha1_hat	100	0	0.794	0.635	−0.550	0.785	2.855
alpha2_hat	100	0	0.117	0.064	−0.036	0.113	0.357
alpha3_hat	100	0	1.000	0.145	0.676	0.988	1.460
gamma0_hat	100	0	2.033	0.742	0.439	2.023	3.761
gamma1_hat	100	0	0.737	1.862	−6.322	0.806	12.258
gamma2_hat	100	0	0.888	0.119	0.609	0.885	1.147
gamma3_hat	100	0	0.894	0.115	0.566	0.894	1.224
theta_hat	100	0	0.125	1.002	−6.217	0.057	3.777
theta_hat_t_stats	100	0	0.167	0.962	−2.034	0.097	2.294
R2_demand	100	0	0.269	0.185	−0.489	0.302	0.527
R2_supply	100	0	0.982	0.003	0.974	0.983	0.989

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.959	0.434	8.882	9.918	11.708
alpha1_hat	100	0	0.941	0.458	−0.074	0.949	2.347
alpha2_hat	100	0	0.104	0.043	−0.022	0.102	0.237
alpha3_hat	100	0	1.001	0.102	0.755	0.998	1.358
gamma0_hat	100	0	1.634	0.644	−0.249	1.580	3.173
gamma1_hat	100	0	0.834	1.274	−2.316	0.828	7.457
gamma2_hat	100	0	0.928	0.099	0.660	0.919	1.195
gamma3_hat	100	0	0.931	0.097	0.676	0.929	1.167
theta_hat	100	0	0.186	0.674	−3.012	0.168	2.364
theta_hat_t_stats	100	0	0.400	1.027	−2.723	0.375	2.559
R2_demand	100	0	0.264	0.137	−0.149	0.274	0.532
R2_supply	100	0	0.980	0.003	0.968	0.980	0.987

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.031	0.176	9.642	10.023	10.461
alpha1_hat	100	0	1.010	0.190	0.643	1.021	1.701
alpha2_hat	100	0	0.101	0.019	0.043	0.098	0.152
alpha3_hat	100	0	1.008	0.037	0.932	1.008	1.111
gamma0_hat	100	0	1.159	0.325	0.402	1.156	2.169
gamma1_hat	100	0	0.898	0.380	−0.209	0.910	1.728
gamma2_hat	100	0	0.979	0.049	0.836	0.979	1.093
gamma3_hat	100	0	0.980	0.045	0.870	0.984	1.106
theta_hat	100	0	0.223	0.196	−0.265	0.211	0.752
theta_hat_t_stats	100	0	1.164	0.947	−1.412	1.200	3.185
R2_demand	100	0	0.264	0.056	0.134	0.271	0.373
R2_supply	100	0	0.978	0.002	0.973	0.977	0.981

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.008	0.132	9.671	10.024	10.394
alpha1_hat	100	0	1.011	0.132	0.646	1.015	1.329
alpha2_hat	100	0	0.099	0.012	0.069	0.098	0.137
alpha3_hat	100	0	0.999	0.030	0.918	1.001	1.077
gamma0_hat	100	0	1.019	0.202	0.493	1.024	1.520
gamma1_hat	100	0	0.877	0.251	0.396	0.862	1.650
gamma2_hat	100	0	0.997	0.029	0.921	0.996	1.061
gamma3_hat	100	0	0.998	0.030	0.918	0.994	1.056
theta_hat	100	0	0.259	0.135	−0.127	0.253	0.537
theta_hat_t_stats	100	0	1.942	0.952	−1.111	1.920	3.797
R2_demand	100	0	0.276	0.042	0.161	0.276	0.375
R2_supply	100	0	0.977	0.001	0.974	0.977	0.980

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.995	0.092	9.780	10.005	10.230
alpha1_hat	100	0	0.988	0.087	0.790	0.990	1.212
alpha2_hat	100	0	0.101	0.008	0.081	0.101	0.120
alpha3_hat	100	0	0.999	0.021	0.942	0.998	1.052
gamma0_hat	100	0	1.007	0.115	0.715	1.004	1.270
gamma1_hat	100	0	0.938	0.152	0.592	0.944	1.256
gamma2_hat	100	0	1.001	0.018	0.959	1.000	1.047
gamma3_hat	100	0	0.999	0.018	0.955	0.998	1.038
theta_hat	100	0	0.229	0.072	0.072	0.227	0.411
theta_hat_t_stats	100	0	2.849	0.868	0.964	2.783	5.225
R2_demand	100	0	0.279	0.026	0.191	0.279	0.337
R2_supply	100	0	0.977	0.001	0.975	0.977	0.979

\(\alpha_2 = 0.5\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.931	0.852	7.610	9.913	12.363
alpha1_hat	100	0	0.945	2.071	−5.565	0.842	6.752
alpha2_hat	100	0	0.494	0.218	−0.055	0.491	1.175
alpha3_hat	100	0	0.991	0.212	0.508	0.965	1.470
gamma0_hat	100	0	2.730	0.906	0.337	2.706	4.949
gamma1_hat	100	0	−0.168	4.818	−41.311	0.334	4.985
gamma2_hat	100	0	0.794	0.151	0.450	0.802	1.113
gamma3_hat	100	0	0.792	0.156	0.350	0.816	1.307
theta_hat	100	0	0.150	0.797	−0.721	0.058	6.350
theta_hat_t_stats	100	0	0.095	0.983	−2.438	0.169	2.315
R2_demand	100	0	0.366	0.272	−0.637	0.422	0.733
R2_supply	100	0	0.981	0.005	0.968	0.982	0.992

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.000	0.609	8.668	9.966	11.644
alpha1_hat	100	0	0.873	1.411	−2.676	0.841	4.144
alpha2_hat	100	0	0.514	0.145	0.207	0.512	1.042
alpha3_hat	100	0	1.013	0.139	0.662	1.010	1.360
gamma0_hat	100	0	2.129	0.893	−0.858	2.289	4.047
gamma1_hat	100	0	0.483	1.588	−4.342	0.465	5.354
gamma2_hat	100	0	0.878	0.135	0.655	0.867	1.264
gamma3_hat	100	0	0.870	0.135	0.597	0.860	1.208
theta_hat	100	0	0.115	0.309	−0.489	0.099	0.992
theta_hat_t_stats	100	0	0.365	1.014	−2.245	0.368	3.071
R2_demand	100	0	0.411	0.176	−0.371	0.446	0.713
R2_supply	100	0	0.977	0.004	0.963	0.977	0.987

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.971	0.392	9.083	9.932	11.142
alpha1_hat	100	0	0.983	1.008	−1.916	1.021	3.446
alpha2_hat	100	0	0.498	0.106	0.255	0.489	0.800
alpha3_hat	100	0	0.983	0.095	0.814	0.981	1.286
gamma0_hat	100	0	1.435	0.610	−0.478	1.446	3.056
gamma1_hat	100	0	0.520	1.315	−2.886	0.618	3.530
gamma2_hat	100	0	0.952	0.086	0.726	0.947	1.186
gamma3_hat	100	0	0.956	0.087	0.768	0.951	1.242
theta_hat	100	0	0.217	0.234	−0.298	0.206	0.968
theta_hat_t_stats	100	0	0.954	0.988	−1.847	0.940	3.169
R2_demand	100	0	0.426	0.108	0.137	0.451	0.643
R2_supply	100	0	0.973	0.004	0.960	0.974	0.983

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.028	0.204	9.613	10.024	10.608
alpha1_hat	100	0	1.011	0.439	0.159	1.018	2.029
alpha2_hat	100	0	0.503	0.053	0.384	0.510	0.622
alpha3_hat	100	0	1.010	0.046	0.915	1.012	1.112
gamma0_hat	100	0	1.074	0.312	0.328	1.102	2.039
gamma1_hat	100	0	0.736	0.581	−0.649	0.713	2.757
gamma2_hat	100	0	0.991	0.046	0.860	0.988	1.120
gamma3_hat	100	0	0.992	0.042	0.882	0.992	1.110
theta_hat	100	0	0.232	0.111	−0.177	0.216	0.527
theta_hat_t_stats	100	0	2.441	1.055	−1.913	2.391	5.832
R2_demand	100	0	0.425	0.045	0.296	0.425	0.511
R2_supply	100	0	0.970	0.003	0.962	0.970	0.977

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.001	0.135	9.705	9.999	10.503
alpha1_hat	100	0	1.015	0.304	0.296	1.053	1.931
alpha2_hat	100	0	0.499	0.031	0.434	0.495	0.592
alpha3_hat	100	0	1.002	0.030	0.923	1.002	1.124
gamma0_hat	100	0	1.026	0.212	0.532	1.033	1.526
gamma1_hat	100	0	0.796	0.364	0.020	0.817	1.711
gamma2_hat	100	0	0.996	0.030	0.930	0.995	1.064
gamma3_hat	100	0	0.997	0.030	0.906	0.997	1.071
theta_hat	100	0	0.231	0.065	0.045	0.242	0.337
theta_hat_t_stats	100	0	3.491	0.935	0.712	3.626	5.046
R2_demand	100	0	0.429	0.035	0.313	0.426	0.516
R2_supply	100	0	0.970	0.002	0.965	0.970	0.974

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.001	0.086	9.814	9.999	10.170
alpha1_hat	100	0	1.027	0.208	0.573	1.011	1.535
alpha2_hat	100	0	0.498	0.024	0.444	0.498	0.558
alpha3_hat	100	0	1.001	0.021	0.959	0.999	1.056
gamma0_hat	100	0	1.015	0.144	0.634	1.020	1.406
gamma1_hat	100	0	0.891	0.239	0.253	0.897	1.489
gamma2_hat	100	0	0.998	0.021	0.953	0.998	1.058
gamma3_hat	100	0	0.996	0.022	0.941	0.996	1.061
theta_hat	100	0	0.216	0.040	0.128	0.218	0.308
theta_hat_t_stats	100	0	5.245	0.926	3.098	5.296	7.701
R2_demand	100	0	0.427	0.022	0.380	0.429	0.481
R2_supply	100	0	0.970	0.001	0.967	0.970	0.973

\(\alpha_2 = 1.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.040	1.033	8.325	9.983	14.154
alpha1_hat	100	0	0.732	3.527	−7.984	0.989	13.497
alpha2_hat	100	0	1.034	0.395	−0.040	0.982	2.165
alpha3_hat	100	0	1.018	0.228	0.547	1.015	2.066
gamma0_hat	100	0	2.806	0.903	0.666	2.748	4.949
gamma1_hat	100	0	−0.049	5.598	−38.026	0.477	15.426
gamma2_hat	100	0	0.805	0.160	0.407	0.807	1.224
gamma3_hat	100	0	0.816	0.169	0.458	0.793	1.311
theta_hat	100	0	0.031	0.510	−1.451	−0.023	2.762
theta_hat_t_stats	100	0	−0.021	1.158	−3.269	−0.077	3.272
R2_demand	100	0	0.442	0.271	−1.045	0.510	0.773
R2_supply	100	0	0.979	0.006	0.960	0.979	0.990

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.888	0.665	8.647	9.810	11.863
alpha1_hat	100	0	1.235	2.322	−4.598	1.410	5.977
alpha2_hat	100	0	0.950	0.277	0.235	0.969	1.804
alpha3_hat	100	0	0.979	0.162	0.634	0.967	1.363
gamma0_hat	100	0	2.169	0.833	0.123	2.095	4.067
gamma1_hat	100	0	0.105	3.702	−16.598	0.670	8.773
gamma2_hat	100	0	0.863	0.123	0.552	0.868	1.261
gamma3_hat	100	0	0.880	0.136	0.585	0.877	1.282
theta_hat	100	0	0.131	0.405	−0.622	0.078	2.151
theta_hat_t_stats	100	0	0.299	1.258	−2.383	0.305	3.226
R2_demand	100	0	0.474	0.143	−0.081	0.508	0.740
R2_supply	100	0	0.975	0.005	0.957	0.976	0.985

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.989	0.402	9.067	9.978	10.821
alpha1_hat	100	0	0.892	1.662	−2.511	0.818	5.197
alpha2_hat	100	0	1.010	0.174	0.651	1.021	1.376
alpha3_hat	100	0	1.008	0.093	0.737	1.010	1.240
gamma0_hat	100	0	1.517	0.639	0.021	1.582	2.956
gamma1_hat	100	0	0.650	1.603	−2.989	0.516	4.405
gamma2_hat	100	0	0.949	0.100	0.708	0.943	1.256
gamma3_hat	100	0	0.943	0.095	0.733	0.946	1.264
theta_hat	100	0	0.155	0.173	−0.212	0.147	0.508
theta_hat_t_stats	100	0	0.807	0.946	−1.174	0.819	2.895
R2_demand	100	0	0.475	0.105	0.002	0.487	0.678
R2_supply	100	0	0.971	0.005	0.956	0.972	0.980

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.988	0.171	9.578	9.975	10.431
alpha1_hat	100	0	0.821	0.715	−0.816	0.789	2.254
alpha2_hat	100	0	1.015	0.078	0.850	1.014	1.272
alpha3_hat	100	0	0.997	0.042	0.893	1.000	1.083
gamma0_hat	100	0	1.050	0.306	0.317	1.052	1.788
gamma1_hat	100	0	0.754	0.748	−0.994	0.768	2.583
gamma2_hat	100	0	0.994	0.044	0.871	0.993	1.093
gamma3_hat	100	0	0.994	0.043	0.889	0.994	1.104
theta_hat	100	0	0.217	0.077	0.038	0.224	0.380
theta_hat_t_stats	100	0	2.648	0.865	0.487	2.709	4.435
R2_demand	100	0	0.473	0.043	0.342	0.479	0.554
R2_supply	100	0	0.968	0.003	0.961	0.968	0.974

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.996	0.145	9.645	9.980	10.376
alpha1_hat	100	0	1.038	0.491	0.048	1.017	2.282
alpha2_hat	100	0	0.995	0.058	0.795	0.986	1.122
alpha3_hat	100	0	1.000	0.032	0.908	1.001	1.091
gamma0_hat	100	0	0.999	0.215	0.343	1.023	1.482
gamma1_hat	100	0	0.788	0.611	−0.696	0.839	2.254
gamma2_hat	100	0	1.000	0.034	0.926	0.996	1.079
gamma3_hat	100	0	0.997	0.031	0.906	1.000	1.107
theta_hat	100	0	0.220	0.062	0.066	0.218	0.390
theta_hat_t_stats	100	0	3.735	0.943	1.290	3.712	5.943
R2_demand	100	0	0.479	0.035	0.380	0.483	0.534
R2_supply	100	0	0.967	0.002	0.963	0.967	0.971

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.992	0.080	9.850	9.989	10.241
alpha1_hat	100	0	0.987	0.308	0.308	0.955	2.050
alpha2_hat	100	0	0.999	0.032	0.921	1.004	1.083
alpha3_hat	100	0	0.999	0.020	0.950	0.998	1.046
gamma0_hat	100	0	1.021	0.131	0.673	1.019	1.308
gamma1_hat	100	0	0.915	0.338	−0.032	0.936	1.649
gamma2_hat	100	0	0.999	0.020	0.962	0.997	1.046
gamma3_hat	100	0	0.996	0.020	0.938	0.997	1.047
theta_hat	100	0	0.205	0.034	0.118	0.204	0.296
theta_hat_t_stats	100	0	5.632	0.825	3.389	5.662	7.723
R2_demand	100	0	0.472	0.020	0.413	0.475	0.513
R2_supply	100	0	0.968	0.001	0.964	0.968	0.970

\(\alpha_2 = 5.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.002	1.058	7.983	9.898	14.800
alpha1_hat	100	0	1.377	15.017	−48.230	0.894	38.341
alpha2_hat	100	0	4.940	1.918	0.544	4.849	15.191
alpha3_hat	100	0	1.006	0.242	0.572	0.991	2.311
gamma0_hat	100	0	2.639	1.233	−1.461	2.691	7.090
gamma1_hat	100	0	−5.666	22.525	−117.822	−0.387	28.257
gamma2_hat	100	0	0.819	0.199	0.173	0.800	1.507
gamma3_hat	100	0	0.832	0.186	0.267	0.810	1.368
theta_hat	100	0	0.114	0.557	−0.924	0.035	2.744
theta_hat_t_stats	100	0	0.052	1.136	−3.250	0.123	2.813
R2_demand	100	0	0.506	0.292	−1.126	0.570	0.816
R2_supply	100	0	0.975	0.006	0.956	0.976	0.987

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.019	0.671	8.679	10.062	12.231
alpha1_hat	100	0	2.664	10.353	−18.538	1.161	33.037
alpha2_hat	100	0	4.837	1.178	1.936	4.857	7.383
alpha3_hat	100	0	1.002	0.139	0.698	0.996	1.357
gamma0_hat	100	0	2.127	0.747	−0.080	2.126	4.044
gamma1_hat	100	0	−1.843	10.331	−42.356	−1.027	26.998
gamma2_hat	100	0	0.869	0.133	0.465	0.872	1.300
gamma3_hat	100	0	0.870	0.136	0.513	0.876	1.219
theta_hat	100	0	0.112	0.237	−0.339	0.096	1.154
theta_hat_t_stats	100	0	0.397	0.873	−1.644	0.489	2.782
R2_demand	100	0	0.507	0.151	−0.049	0.532	0.741
R2_supply	100	0	0.973	0.005	0.958	0.974	0.983

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.955	0.387	9.235	9.913	11.116
alpha1_hat	100	0	0.953	6.612	−20.606	1.011	18.557
alpha2_hat	100	0	4.949	0.771	3.250	4.930	7.343
alpha3_hat	100	0	0.980	0.087	0.739	0.973	1.348
gamma0_hat	100	0	1.523	0.665	−0.546	1.614	2.793
gamma1_hat	100	0	−1.884	6.949	−23.961	−1.222	16.818
gamma2_hat	100	0	0.943	0.101	0.754	0.933	1.219
gamma3_hat	100	0	0.938	0.095	0.723	0.938	1.192
theta_hat	100	0	0.191	0.169	−0.234	0.173	0.692
theta_hat_t_stats	100	0	1.087	0.923	−1.760	1.061	2.948
R2_demand	100	0	0.521	0.102	0.148	0.532	0.682
R2_supply	100	0	0.969	0.006	0.950	0.970	0.978

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.982	0.193	9.560	9.971	10.435
alpha1_hat	100	0	1.092	3.330	−6.629	0.974	7.706
alpha2_hat	100	0	4.972	0.378	4.148	5.007	5.920
alpha3_hat	100	0	0.992	0.049	0.891	0.986	1.130
gamma0_hat	100	0	1.028	0.327	0.107	1.020	1.731
gamma1_hat	100	0	−0.354	3.578	−8.907	−0.572	9.172
gamma2_hat	100	0	0.997	0.047	0.887	1.001	1.122
gamma3_hat	100	0	1.004	0.046	0.897	1.003	1.104
theta_hat	100	0	0.225	0.077	0.017	0.228	0.388
theta_hat_t_stats	100	0	2.969	0.938	0.255	3.125	5.071
R2_demand	100	0	0.521	0.039	0.432	0.517	0.609
R2_supply	100	0	0.965	0.003	0.957	0.965	0.970

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.999	0.134	9.692	10.002	10.278
alpha1_hat	100	0	1.050	2.303	−6.558	1.026	6.791
alpha2_hat	100	0	4.995	0.248	4.188	4.964	5.820
alpha3_hat	100	0	1.002	0.030	0.929	1.001	1.072
gamma0_hat	100	0	1.010	0.214	0.489	1.020	1.528
gamma1_hat	100	0	0.021	2.175	−5.899	0.050	4.856
gamma2_hat	100	0	1.000	0.033	0.907	0.997	1.096
gamma3_hat	100	0	0.992	0.031	0.913	0.997	1.067
theta_hat	100	0	0.218	0.051	0.099	0.221	0.353
theta_hat_t_stats	100	0	4.156	0.879	2.102	4.250	6.452
R2_demand	100	0	0.519	0.029	0.437	0.521	0.587
R2_supply	100	0	0.964	0.002	0.958	0.964	0.970

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.000	0.084	9.818	10.003	10.194
alpha1_hat	100	0	0.896	1.299	−2.603	1.018	4.193
alpha2_hat	100	0	5.009	0.169	4.558	5.006	5.406
alpha3_hat	100	0	1.001	0.019	0.951	1.001	1.055
gamma0_hat	100	0	1.006	0.123	0.676	1.017	1.341
gamma1_hat	100	0	0.677	1.371	−2.389	0.750	4.054
gamma2_hat	100	0	0.999	0.020	0.954	0.998	1.051
gamma3_hat	100	0	0.997	0.019	0.957	0.998	1.037
theta_hat	100	0	0.206	0.034	0.114	0.205	0.313
theta_hat_t_stats	100	0	6.296	0.929	3.542	6.268	8.897
R2_demand	100	0	0.519	0.017	0.475	0.520	0.551
R2_supply	100	0	0.964	0.001	0.962	0.964	0.967

\(\alpha_2 = 20.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.907	0.938	7.866	9.809	12.850
alpha1_hat	100	0	1.370	51.562	−120.993	−5.489	170.972
alpha2_hat	100	0	19.581	6.126	3.832	19.461	40.350
alpha3_hat	100	0	0.994	0.232	0.524	0.955	1.846
gamma0_hat	100	0	2.782	1.020	−0.130	2.758	5.169
gamma1_hat	100	0	−6.241	71.822	−372.320	1.326	118.587
gamma2_hat	100	0	0.799	0.166	0.402	0.802	1.334
gamma3_hat	100	0	0.808	0.163	0.510	0.788	1.247
theta_hat	100	0	0.000	0.397	−0.679	−0.079	2.100
theta_hat_t_stats	100	0	−0.192	1.040	−2.780	−0.294	2.484
R2_demand	100	0	0.504	0.230	−0.385	0.553	0.813
R2_supply	100	0	0.975	0.006	0.958	0.976	0.987

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.964	0.590	8.849	9.864	12.076
alpha1_hat	100	0	−6.842	38.993	−106.509	−8.018	94.391
alpha2_hat	100	0	20.716	4.666	11.087	20.285	34.440
alpha3_hat	100	0	0.994	0.129	0.703	0.993	1.496
gamma0_hat	100	0	2.064	0.860	−0.807	2.162	3.949
gamma1_hat	100	0	−6.651	38.958	−137.241	−5.655	148.931
gamma2_hat	100	0	0.885	0.135	0.576	0.888	1.293
gamma3_hat	100	0	0.863	0.129	0.546	0.878	1.236
theta_hat	100	0	0.098	0.223	−0.574	0.078	0.722
theta_hat_t_stats	100	0	0.404	0.959	−2.281	0.360	2.534
R2_demand	100	0	0.526	0.168	−0.418	0.558	0.786
R2_supply	100	0	0.972	0.006	0.952	0.973	0.981

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.041	0.450	9.145	10.047	11.300
alpha1_hat	100	0	3.898	32.444	−76.175	2.590	80.157
alpha2_hat	100	0	19.927	3.680	12.924	19.748	32.442
alpha3_hat	100	0	1.025	0.102	0.792	1.028	1.270
gamma0_hat	100	0	1.611	0.562	0.131	1.690	3.150
gamma1_hat	100	0	−11.447	25.385	−72.824	−11.050	45.139
gamma2_hat	100	0	0.928	0.085	0.652	0.915	1.207
gamma3_hat	100	0	0.939	0.091	0.716	0.936	1.171
theta_hat	100	0	0.184	0.145	−0.124	0.170	0.559
theta_hat_t_stats	100	0	1.092	0.796	−0.992	1.093	2.576
R2_demand	100	0	0.517	0.094	0.251	0.529	0.722
R2_supply	100	0	0.968	0.005	0.954	0.969	0.977

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.986	0.172	9.642	9.959	10.463
alpha1_hat	100	0	1.846	13.554	−32.313	1.997	35.088
alpha2_hat	100	0	19.849	1.481	16.789	19.801	23.422
alpha3_hat	100	0	0.995	0.044	0.904	0.992	1.124
gamma0_hat	100	0	1.119	0.271	0.221	1.121	1.718
gamma1_hat	100	0	−5.323	12.637	−34.809	−6.603	30.998
gamma2_hat	100	0	0.988	0.039	0.903	0.982	1.095
gamma3_hat	100	0	0.989	0.045	0.892	0.986	1.126
theta_hat	100	0	0.217	0.074	0.051	0.228	0.388
theta_hat_t_stats	100	0	2.947	0.942	0.767	3.098	5.131
R2_demand	100	0	0.531	0.041	0.385	0.536	0.609
R2_supply	100	0	0.965	0.002	0.955	0.965	0.970

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.989	0.154	9.663	9.990	10.370
alpha1_hat	100	0	2.484	8.549	−26.399	3.687	21.425
alpha2_hat	100	0	19.802	1.119	17.548	19.748	23.647
alpha3_hat	100	0	0.999	0.034	0.918	1.000	1.075
gamma0_hat	100	0	1.024	0.191	0.566	1.011	1.494
gamma1_hat	100	0	−2.420	9.483	−27.181	−3.119	18.414
gamma2_hat	100	0	0.999	0.029	0.916	0.998	1.085
gamma3_hat	100	0	0.994	0.031	0.925	0.996	1.060
theta_hat	100	0	0.214	0.053	0.090	0.209	0.344
theta_hat_t_stats	100	0	4.118	0.887	1.869	4.080	5.951
R2_demand	100	0	0.530	0.029	0.470	0.531	0.594
R2_supply	100	0	0.964	0.002	0.958	0.964	0.968

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.007	0.092	9.755	10.000	10.283
alpha1_hat	100	0	0.720	5.440	−13.112	0.422	12.155
alpha2_hat	100	0	20.050	0.645	18.084	20.056	21.485
alpha3_hat	100	0	1.003	0.022	0.949	1.003	1.072
gamma0_hat	100	0	0.996	0.133	0.641	0.998	1.282
gamma1_hat	100	0	−0.020	5.373	−13.535	0.016	9.925
gamma2_hat	100	0	0.999	0.019	0.958	0.999	1.053
gamma3_hat	100	0	1.001	0.020	0.959	1.001	1.060
theta_hat	100	0	0.206	0.032	0.131	0.203	0.295
theta_hat_t_stats	100	0	6.423	0.901	4.262	6.388	8.706
R2_demand	100	0	0.530	0.021	0.467	0.532	0.578
R2_supply	100	0	0.963	0.001	0.960	0.963	0.967

\(\theta = 0.33\)

\(\alpha_2 = 0.1\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.101	0.903	7.916	10.022	12.702
alpha1_hat	100	0	1.053	1.063	−1.100	0.896	4.684
alpha2_hat	100	0	0.102	0.093	−0.171	0.098	0.323
alpha3_hat	100	0	1.003	0.219	0.569	0.991	1.623
gamma0_hat	100	0	3.050	0.971	−0.051	3.104	4.989
gamma1_hat	100	0	−0.328	10.076	−93.934	0.906	11.701
gamma2_hat	100	0	0.768	0.161	0.293	0.748	1.236
gamma3_hat	100	0	0.760	0.137	0.439	0.760	1.133
theta_hat	100	0	0.476	4.086	−5.673	−0.041	36.647
theta_hat_t_stats	100	0	−0.076	0.967	−2.664	−0.063	2.492
R2_demand	100	0	0.169	0.305	−0.935	0.247	0.609
R2_supply	100	0	0.986	0.004	0.975	0.986	0.993

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.942	0.645	8.511	9.888	11.803
alpha1_hat	100	0	1.035	0.659	−1.098	1.009	2.949
alpha2_hat	100	0	0.094	0.060	−0.039	0.092	0.305
alpha3_hat	100	0	1.003	0.158	0.666	0.989	1.558
gamma0_hat	100	0	2.150	0.882	−1.646	2.183	3.732
gamma1_hat	100	0	1.378	6.796	−15.452	0.796	51.772
gamma2_hat	100	0	0.872	0.139	0.605	0.845	1.320
gamma3_hat	100	0	0.877	0.144	0.587	0.853	1.424
theta_hat	100	0	−0.102	3.410	−26.026	0.169	8.604
theta_hat_t_stats	100	0	0.300	0.965	−2.071	0.363	2.250
R2_demand	100	0	0.245	0.153	−0.357	0.283	0.542
R2_supply	100	0	0.983	0.004	0.965	0.984	0.989

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.021	0.418	9.172	9.970	11.266
alpha1_hat	100	0	1.039	0.462	−0.247	0.990	2.050
alpha2_hat	100	0	0.097	0.042	−0.003	0.096	0.235
alpha3_hat	100	0	1.008	0.096	0.801	1.004	1.253
gamma0_hat	100	0	1.540	0.564	−0.050	1.607	2.841
gamma1_hat	100	0	0.541	1.599	−11.989	0.731	3.955
gamma2_hat	100	0	0.937	0.084	0.739	0.926	1.149
gamma3_hat	100	0	0.949	0.088	0.748	0.951	1.153
theta_hat	100	0	0.450	0.787	−1.252	0.331	6.558
theta_hat_t_stats	100	0	0.801	0.772	−0.915	0.735	2.460
R2_demand	100	0	0.230	0.134	−0.151	0.238	0.537
R2_supply	100	0	0.981	0.003	0.972	0.982	0.987

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.987	0.203	9.377	9.972	10.663
alpha1_hat	100	0	1.005	0.200	0.332	1.003	1.444
alpha2_hat	100	0	0.099	0.020	0.053	0.101	0.155
alpha3_hat	100	0	1.004	0.048	0.843	1.004	1.118
gamma0_hat	100	0	1.140	0.297	0.404	1.150	1.827
gamma1_hat	100	0	0.852	0.405	−0.353	0.846	1.758
gamma2_hat	100	0	0.981	0.049	0.852	0.981	1.106
gamma3_hat	100	0	0.994	0.037	0.914	0.992	1.092
theta_hat	100	0	0.383	0.212	−0.141	0.382	1.159
theta_hat_t_stats	100	0	1.876	0.974	−0.772	2.002	4.150
R2_demand	100	0	0.241	0.058	0.101	0.249	0.371
R2_supply	100	0	0.979	0.002	0.975	0.979	0.982

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.010	0.136	9.632	10.018	10.284
alpha1_hat	100	0	1.010	0.130	0.719	1.001	1.343
alpha2_hat	100	0	0.099	0.014	0.067	0.098	0.142
alpha3_hat	100	0	0.998	0.033	0.931	0.999	1.087
gamma0_hat	100	0	1.070	0.187	0.465	1.118	1.449
gamma1_hat	100	0	0.858	0.315	0.014	0.839	1.814
gamma2_hat	100	0	0.991	0.030	0.917	0.990	1.100
gamma3_hat	100	0	0.991	0.027	0.934	0.992	1.063
theta_hat	100	0	0.386	0.159	−0.132	0.379	0.861
theta_hat_t_stats	100	0	2.743	1.092	−0.998	2.760	5.375
R2_demand	100	0	0.230	0.042	0.126	0.223	0.333
R2_supply	100	0	0.979	0.001	0.975	0.979	0.981

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.996	0.094	9.756	10.009	10.186
alpha1_hat	100	0	0.984	0.093	0.700	0.981	1.208
alpha2_hat	100	0	0.101	0.009	0.079	0.101	0.121
alpha3_hat	100	0	1.001	0.021	0.948	1.002	1.060
gamma0_hat	100	0	1.012	0.132	0.627	1.009	1.283
gamma1_hat	100	0	0.989	0.175	0.510	0.993	1.437
gamma2_hat	100	0	0.998	0.019	0.950	1.000	1.048
gamma3_hat	100	0	0.998	0.019	0.957	0.997	1.041
theta_hat	100	0	0.335	0.090	0.066	0.327	0.570
theta_hat_t_stats	100	0	3.868	0.976	0.890	3.892	6.185
R2_demand	100	0	0.240	0.027	0.161	0.242	0.292
R2_supply	100	0	0.978	0.001	0.976	0.978	0.980

\(\alpha_2 = 0.5\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.788	0.869	7.639	9.751	13.200
alpha1_hat	100	0	0.846	2.077	−3.651	0.938	6.905
alpha2_hat	100	0	0.484	0.233	−0.058	0.490	1.293
alpha3_hat	100	0	0.971	0.219	0.492	0.951	1.737
gamma0_hat	100	0	2.877	0.940	0.285	2.796	5.486
gamma1_hat	100	0	−0.944	21.296	−142.577	0.759	88.585
gamma2_hat	100	0	0.798	0.153	0.404	0.803	1.215
gamma3_hat	100	0	0.786	0.147	0.442	0.777	1.108
theta_hat	100	0	0.375	4.051	−13.291	0.030	27.103
theta_hat_t_stats	100	0	0.113	1.038	−3.937	0.066	2.469
R2_demand	100	0	0.366	0.273	−1.213	0.436	0.762
R2_supply	100	0	0.983	0.004	0.971	0.983	0.990

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.124	0.601	8.625	10.097	11.521
alpha1_hat	100	0	0.972	1.435	−3.407	0.881	5.203
alpha2_hat	100	0	0.523	0.162	0.116	0.529	0.973
alpha3_hat	100	0	1.044	0.148	0.716	1.051	1.519
gamma0_hat	100	0	2.179	0.700	0.521	2.290	4.102
gamma1_hat	100	0	0.683	1.792	−4.501	0.586	6.677
gamma2_hat	100	0	0.877	0.108	0.658	0.882	1.126
gamma3_hat	100	0	0.870	0.124	0.529	0.860	1.239
theta_hat	100	0	0.182	0.311	−0.618	0.170	1.398
theta_hat_t_stats	100	0	0.538	0.820	−1.567	0.700	2.075
R2_demand	100	0	0.314	0.194	−0.334	0.351	0.618
R2_supply	100	0	0.980	0.004	0.968	0.981	0.989

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.969	0.451	8.923	9.933	11.168
alpha1_hat	100	0	0.994	1.062	−2.433	0.846	4.063
alpha2_hat	100	0	0.496	0.109	0.221	0.488	0.786
alpha3_hat	100	0	0.999	0.116	0.726	1.009	1.273
gamma0_hat	100	0	1.713	0.535	0.128	1.717	2.975
gamma1_hat	100	0	0.585	1.522	−3.143	0.668	3.671
gamma2_hat	100	0	0.917	0.081	0.709	0.908	1.179
gamma3_hat	100	0	0.934	0.094	0.700	0.932	1.166
theta_hat	100	0	0.288	0.261	−0.173	0.259	0.995
theta_hat_t_stats	100	0	1.217	1.047	−0.813	1.158	3.946
R2_demand	100	0	0.357	0.115	0.000	0.379	0.556
R2_supply	100	0	0.977	0.004	0.969	0.977	0.985

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.989	0.216	9.527	9.985	10.570
alpha1_hat	100	0	0.921	0.428	−0.146	0.935	2.314
alpha2_hat	100	0	0.506	0.054	0.332	0.504	0.620
alpha3_hat	100	0	1.000	0.042	0.899	1.000	1.119
gamma0_hat	100	0	1.116	0.279	0.036	1.151	1.686
gamma1_hat	100	0	0.864	0.545	−0.288	0.824	2.054
gamma2_hat	100	0	0.989	0.041	0.888	0.993	1.109
gamma3_hat	100	0	0.989	0.042	0.881	0.985	1.085
theta_hat	100	0	0.334	0.105	0.084	0.334	0.617
theta_hat_t_stats	100	0	3.298	0.901	0.805	3.368	5.172
R2_demand	100	0	0.355	0.058	0.160	0.364	0.475
R2_supply	100	0	0.974	0.002	0.969	0.974	0.978

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.983	0.126	9.699	9.986	10.273
alpha1_hat	100	0	0.951	0.318	0.161	0.927	1.761
alpha2_hat	100	0	0.503	0.034	0.427	0.500	0.587
alpha3_hat	100	0	0.996	0.031	0.916	0.995	1.082
gamma0_hat	100	0	1.018	0.217	0.438	1.033	1.555
gamma1_hat	100	0	0.847	0.392	−0.129	0.863	1.694
gamma2_hat	100	0	1.001	0.030	0.926	1.001	1.090
gamma3_hat	100	0	0.996	0.032	0.918	0.998	1.069
theta_hat	100	0	0.353	0.080	0.174	0.350	0.577
theta_hat_t_stats	100	0	4.880	0.953	2.478	4.947	6.943
R2_demand	100	0	0.366	0.031	0.286	0.368	0.439
R2_supply	100	0	0.973	0.001	0.970	0.973	0.977

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.003	0.085	9.817	9.998	10.200
alpha1_hat	100	0	1.034	0.202	0.571	1.027	1.492
alpha2_hat	100	0	0.497	0.022	0.452	0.499	0.546
alpha3_hat	100	0	1.000	0.021	0.946	1.000	1.058
gamma0_hat	100	0	1.020	0.123	0.714	1.024	1.336
gamma1_hat	100	0	0.841	0.260	0.122	0.851	1.691
gamma2_hat	100	0	0.998	0.017	0.947	0.999	1.039
gamma3_hat	100	0	0.997	0.019	0.953	0.997	1.042
theta_hat	100	0	0.353	0.048	0.173	0.352	0.491
theta_hat_t_stats	100	0	7.786	0.940	3.828	7.718	9.819
R2_demand	100	0	0.359	0.021	0.309	0.361	0.424
R2_supply	100	0	0.973	0.001	0.971	0.973	0.976

\(\alpha_2 = 1.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.881	0.911	7.719	9.780	12.297
alpha1_hat	100	0	0.820	3.832	−10.976	1.218	10.451
alpha2_hat	100	0	0.987	0.444	0.155	0.988	2.274
alpha3_hat	100	0	0.974	0.233	0.323	0.985	1.659
gamma0_hat	100	0	2.865	0.932	−0.045	2.755	5.161
gamma1_hat	100	0	−0.172	5.544	−15.292	−0.002	34.410
gamma2_hat	100	0	0.801	0.161	0.411	0.828	1.157
gamma3_hat	100	0	0.809	0.164	0.424	0.805	1.243
theta_hat	100	0	0.154	0.547	−2.567	0.125	1.698
theta_hat_t_stats	100	0	0.269	0.983	−2.299	0.313	2.433
R2_demand	100	0	0.433	0.229	−0.605	0.487	0.756
R2_supply	100	0	0.981	0.004	0.970	0.981	0.990

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.911	0.619	8.764	9.845	11.944
alpha1_hat	100	0	0.851	2.377	−4.596	0.806	6.231
alpha2_hat	100	0	0.991	0.288	0.353	0.978	1.800
alpha3_hat	100	0	0.999	0.152	0.641	0.992	1.480
gamma0_hat	100	0	2.078	0.864	−0.685	2.031	4.021
gamma1_hat	100	0	0.455	3.207	−8.076	1.032	7.723
gamma2_hat	100	0	0.880	0.129	0.583	0.878	1.271
gamma3_hat	100	0	0.868	0.141	0.544	0.859	1.291
theta_hat	100	0	0.219	0.344	−0.420	0.180	1.063
theta_hat_t_stats	100	0	0.694	1.069	−1.751	0.691	3.124
R2_demand	100	0	0.402	0.166	−0.199	0.436	0.642
R2_supply	100	0	0.978	0.004	0.966	0.978	0.985

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.991	0.399	9.100	9.926	10.992
alpha1_hat	100	0	0.978	1.600	−2.596	1.086	4.918
alpha2_hat	100	0	1.004	0.184	0.606	0.988	1.468
alpha3_hat	100	0	0.998	0.087	0.807	0.986	1.228
gamma0_hat	100	0	1.621	0.605	0.046	1.659	3.814
gamma1_hat	100	0	0.664	1.997	−7.424	0.659	5.592
gamma2_hat	100	0	0.924	0.092	0.610	0.926	1.159
gamma3_hat	100	0	0.931	0.091	0.674	0.915	1.200
theta_hat	100	0	0.268	0.216	−0.273	0.286	1.089
theta_hat_t_stats	100	0	1.289	0.929	−1.035	1.343	3.277
R2_demand	100	0	0.377	0.113	0.060	0.406	0.605
R2_supply	100	0	0.975	0.004	0.961	0.975	0.981

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.009	0.199	9.552	10.022	10.515
alpha1_hat	100	0	1.064	0.807	−1.336	1.050	3.026
alpha2_hat	100	0	0.997	0.092	0.774	0.993	1.273
alpha3_hat	100	0	1.006	0.052	0.901	1.006	1.140
gamma0_hat	100	0	1.079	0.270	0.348	1.070	1.625
gamma1_hat	100	0	0.590	0.923	−1.620	0.617	2.482
gamma2_hat	100	0	0.990	0.039	0.922	0.983	1.092
gamma3_hat	100	0	0.995	0.041	0.902	0.998	1.094
theta_hat	100	0	0.355	0.101	0.145	0.355	0.632
theta_hat_t_stats	100	0	3.849	0.925	1.802	3.835	6.046
R2_demand	100	0	0.392	0.048	0.264	0.393	0.500
R2_supply	100	0	0.972	0.002	0.965	0.972	0.978

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.983	0.130	9.671	9.990	10.252
alpha1_hat	100	0	1.070	0.629	−0.608	1.069	2.884
alpha2_hat	100	0	0.989	0.064	0.812	0.983	1.179
alpha3_hat	100	0	0.996	0.032	0.915	0.996	1.087
gamma0_hat	100	0	1.015	0.225	0.392	1.026	1.454
gamma1_hat	100	0	0.741	0.648	−0.773	0.799	2.350
gamma2_hat	100	0	0.998	0.034	0.937	0.998	1.085
gamma3_hat	100	0	0.998	0.037	0.931	0.992	1.091
theta_hat	100	0	0.354	0.065	0.200	0.351	0.494
theta_hat_t_stats	100	0	5.439	0.846	3.388	5.365	7.324
R2_demand	100	0	0.400	0.034	0.302	0.401	0.492
R2_supply	100	0	0.972	0.002	0.966	0.972	0.975

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.015	0.085	9.826	10.024	10.269
alpha1_hat	100	0	1.057	0.391	−0.222	1.003	2.088
alpha2_hat	100	0	0.997	0.043	0.904	0.998	1.133
alpha3_hat	100	0	1.003	0.020	0.961	1.002	1.064
gamma0_hat	100	0	1.013	0.130	0.662	1.021	1.383
gamma1_hat	100	0	0.852	0.398	0.004	0.844	1.710
gamma2_hat	100	0	0.999	0.019	0.949	0.999	1.045
gamma3_hat	100	0	0.999	0.023	0.946	1.000	1.056
theta_hat	100	0	0.341	0.040	0.244	0.340	0.440
theta_hat_t_stats	100	0	8.495	0.908	5.954	8.520	10.872
R2_demand	100	0	0.395	0.020	0.347	0.395	0.445
R2_supply	100	0	0.972	0.001	0.970	0.972	0.974

\(\alpha_2 = 5.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.155	1.110	8.022	9.940	14.074
alpha1_hat	100	0	−0.743	17.362	−47.100	−1.777	52.841
alpha2_hat	100	0	5.352	1.980	0.878	5.258	10.056
alpha3_hat	100	0	1.028	0.251	0.492	0.996	2.140
gamma0_hat	100	0	3.200	0.909	0.037	3.191	5.759
gamma1_hat	100	0	−1.397	19.524	−88.836	0.319	59.714
gamma2_hat	100	0	0.730	0.152	0.430	0.740	1.112
gamma3_hat	100	0	0.778	0.165	0.291	0.771	1.220
theta_hat	100	0	0.087	0.437	−0.787	0.017	2.224
theta_hat_t_stats	100	0	0.063	0.938	−2.139	0.079	2.313
R2_demand	100	0	0.344	0.381	−1.444	0.452	0.757
R2_supply	100	0	0.980	0.005	0.968	0.981	0.992

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.034	0.656	8.761	9.962	12.255
alpha1_hat	100	0	1.650	12.396	−33.550	0.718	38.354
alpha2_hat	100	0	4.988	1.422	2.300	4.944	9.145
alpha3_hat	100	0	1.001	0.156	0.577	1.020	1.546
gamma0_hat	100	0	2.090	0.828	−0.652	2.157	3.900
gamma1_hat	100	0	−3.650	13.271	−36.075	−2.140	23.745
gamma2_hat	100	0	0.891	0.129	0.605	0.885	1.204
gamma3_hat	100	0	0.866	0.121	0.562	0.857	1.201
theta_hat	100	0	0.253	0.297	−0.265	0.219	1.243
theta_hat_t_stats	100	0	0.869	0.951	−1.571	1.003	2.459
R2_demand	100	0	0.424	0.158	−0.076	0.453	0.721
R2_supply	100	0	0.976	0.005	0.958	0.977	0.986

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.080	0.461	9.105	10.044	11.438
alpha1_hat	100	0	2.168	8.411	−18.957	2.191	21.653
alpha2_hat	100	0	4.968	0.909	2.360	4.973	7.329
alpha3_hat	100	0	1.003	0.094	0.807	0.992	1.269
gamma0_hat	100	0	1.552	0.582	0.117	1.603	2.665
gamma1_hat	100	0	−3.450	9.324	−34.725	−3.329	17.438
gamma2_hat	100	0	0.934	0.096	0.753	0.934	1.152
gamma3_hat	100	0	0.938	0.096	0.704	0.933	1.177
theta_hat	100	0	0.336	0.223	−0.159	0.307	1.191
theta_hat_t_stats	100	0	1.749	0.932	−0.958	1.886	4.108
R2_demand	100	0	0.424	0.107	0.069	0.441	0.604
R2_supply	100	0	0.973	0.004	0.965	0.974	0.981

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.017	0.207	9.502	10.010	10.834
alpha1_hat	100	0	1.106	3.724	−11.821	0.780	11.378
alpha2_hat	100	0	5.009	0.401	4.036	5.032	6.438
alpha3_hat	100	0	0.998	0.050	0.890	1.000	1.130
gamma0_hat	100	0	1.048	0.325	0.246	1.043	1.708
gamma1_hat	100	0	−0.532	4.228	−11.339	−0.248	7.667
gamma2_hat	100	0	0.995	0.051	0.878	0.993	1.125
gamma3_hat	100	0	0.991	0.045	0.877	0.986	1.082
theta_hat	100	0	0.353	0.094	0.123	0.339	0.590
theta_hat_t_stats	100	0	4.240	0.953	1.727	4.229	6.446
R2_demand	100	0	0.435	0.049	0.297	0.443	0.561
R2_supply	100	0	0.970	0.002	0.960	0.970	0.974

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.998	0.146	9.661	10.001	10.377
alpha1_hat	100	0	0.880	2.928	−9.563	0.832	8.123
alpha2_hat	100	0	5.011	0.310	4.243	5.014	6.091
alpha3_hat	100	0	0.998	0.030	0.908	0.999	1.086
gamma0_hat	100	0	1.043	0.227	0.490	1.075	1.538
gamma1_hat	100	0	−0.058	2.869	−7.891	0.000	6.226
gamma2_hat	100	0	0.996	0.034	0.900	1.000	1.083
gamma3_hat	100	0	0.996	0.032	0.931	0.993	1.095
theta_hat	100	0	0.344	0.070	0.201	0.339	0.492
theta_hat_t_stats	100	0	5.959	0.953	3.716	5.980	7.901
R2_demand	100	0	0.437	0.032	0.337	0.438	0.501
R2_supply	100	0	0.970	0.002	0.965	0.970	0.975

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.998	0.088	9.713	9.995	10.212
alpha1_hat	100	0	0.987	1.683	−3.239	0.900	5.071
alpha2_hat	100	0	4.998	0.194	4.540	4.998	5.521
alpha3_hat	100	0	1.001	0.020	0.962	1.003	1.053
gamma0_hat	100	0	1.024	0.154	0.682	1.017	1.523
gamma1_hat	100	0	0.618	1.553	−3.164	0.602	5.249
gamma2_hat	100	0	0.998	0.021	0.933	1.000	1.047
gamma3_hat	100	0	0.997	0.022	0.947	0.996	1.053
theta_hat	100	0	0.334	0.034	0.244	0.333	0.429
theta_hat_t_stats	100	0	9.217	0.766	7.115	9.357	10.854
R2_demand	100	0	0.439	0.023	0.391	0.439	0.495
R2_supply	100	0	0.969	0.001	0.966	0.969	0.972

\(\alpha_2 = 20.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.012	1.402	7.889	9.766	20.673
alpha1_hat	100	0	7.425	85.038	−130.833	7.690	601.521
alpha2_hat	100	0	19.400	7.157	3.583	18.262	41.696
alpha3_hat	100	0	1.006	0.267	0.477	0.984	2.735
gamma0_hat	100	0	2.883	0.997	−0.236	2.871	5.377
gamma1_hat	100	0	−30.850	81.198	−391.959	−18.674	127.774
gamma2_hat	100	0	0.796	0.167	0.373	0.813	1.343
gamma3_hat	100	0	0.812	0.170	0.419	0.799	1.186
theta_hat	100	0	0.208	0.466	−0.685	0.126	2.103
theta_hat_t_stats	100	0	0.371	0.988	−2.155	0.416	2.601
R2_demand	100	0	0.371	0.875	−7.955	0.533	0.791
R2_supply	100	0	0.979	0.004	0.967	0.979	0.988

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.079	0.710	8.357	9.956	13.374
alpha1_hat	100	0	−5.827	50.208	−119.702	1.818	123.228
alpha2_hat	100	0	20.975	6.353	4.808	19.588	36.780
alpha3_hat	100	0	1.019	0.150	0.700	0.997	1.424
gamma0_hat	100	0	2.038	0.801	−0.825	2.119	3.676
gamma1_hat	100	0	−9.338	63.009	−277.901	−4.041	163.699
gamma2_hat	100	0	0.901	0.125	0.556	0.879	1.251
gamma3_hat	100	0	0.870	0.128	0.575	0.857	1.201
theta_hat	100	0	0.234	0.370	−0.621	0.166	2.218
theta_hat_t_stats	100	0	0.808	0.995	−1.592	0.815	4.356
R2_demand	100	0	0.415	0.203	−0.875	0.450	0.720
R2_supply	100	0	0.976	0.005	0.955	0.977	0.985

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.922	0.407	9.079	9.935	10.884
alpha1_hat	100	0	−1.508	28.924	−68.330	−3.907	68.355
alpha2_hat	100	0	19.881	3.396	11.564	19.740	28.292
alpha3_hat	100	0	0.982	0.101	0.768	0.984	1.289
gamma0_hat	100	0	1.622	0.599	0.045	1.676	2.842
gamma1_hat	100	0	−5.032	37.076	−107.607	−6.090	109.824
gamma2_hat	100	0	0.927	0.093	0.666	0.915	1.170
gamma3_hat	100	0	0.933	0.105	0.651	0.932	1.239
theta_hat	100	0	0.278	0.215	−0.353	0.261	1.143
theta_hat_t_stats	100	0	1.491	1.009	−1.826	1.463	3.428
R2_demand	100	0	0.446	0.109	0.103	0.464	0.666
R2_supply	100	0	0.973	0.004	0.962	0.974	0.979

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.014	0.213	9.553	10.005	10.726
alpha1_hat	100	0	−0.823	13.567	−28.407	−2.822	40.858
alpha2_hat	100	0	20.238	1.701	16.009	20.199	24.180
alpha3_hat	100	0	1.003	0.048	0.920	1.002	1.161
gamma0_hat	100	0	1.076	0.285	0.199	1.116	1.692
gamma1_hat	100	0	−4.559	14.751	−59.925	−3.706	28.596
gamma2_hat	100	0	0.991	0.046	0.898	0.997	1.109
gamma3_hat	100	0	1.000	0.042	0.912	0.996	1.116
theta_hat	100	0	0.347	0.086	0.153	0.346	0.685
theta_hat_t_stats	100	0	4.300	0.874	2.278	4.263	6.952
R2_demand	100	0	0.450	0.053	0.302	0.458	0.542
R2_supply	100	0	0.969	0.002	0.963	0.969	0.974

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.988	0.137	9.717	9.973	10.406
alpha1_hat	100	0	1.148	10.368	−31.475	0.356	30.391
alpha2_hat	100	0	19.959	1.206	17.236	19.892	23.249
alpha3_hat	100	0	0.999	0.031	0.925	0.999	1.086
gamma0_hat	100	0	0.990	0.195	0.552	0.971	1.579
gamma1_hat	100	0	−2.194	9.683	−29.166	−2.142	19.494
gamma2_hat	100	0	1.001	0.028	0.904	1.000	1.067
gamma3_hat	100	0	0.998	0.033	0.918	0.999	1.067
theta_hat	100	0	0.348	0.057	0.228	0.347	0.506
theta_hat_t_stats	100	0	6.092	0.835	4.292	5.991	8.040
R2_demand	100	0	0.446	0.035	0.350	0.447	0.527
R2_supply	100	0	0.969	0.001	0.966	0.969	0.973

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.001	0.098	9.752	10.008	10.213
alpha1_hat	100	0	1.032	6.687	−12.985	1.126	13.148
alpha2_hat	100	0	20.003	0.827	17.757	19.938	22.084
alpha3_hat	100	0	1.001	0.022	0.938	1.002	1.048
gamma0_hat	100	0	1.018	0.139	0.707	1.026	1.318
gamma1_hat	100	0	−1.843	6.898	−22.752	−1.159	16.108
gamma2_hat	100	0	0.998	0.021	0.959	0.999	1.049
gamma3_hat	100	0	0.999	0.020	0.954	1.000	1.045
theta_hat	100	0	0.342	0.042	0.213	0.335	0.489
theta_hat_t_stats	100	0	9.586	0.935	6.552	9.565	12.395
R2_demand	100	0	0.447	0.022	0.389	0.449	0.490
R2_supply	100	0	0.969	0.001	0.967	0.969	0.971

\(\theta = 0.5\)

\(\alpha_2 = 0.1\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.068	1.045	7.915	9.982	13.936
alpha1_hat	100	0	1.002	1.373	−1.912	1.049	7.658
alpha2_hat	100	0	0.104	0.129	−0.276	0.093	0.585
alpha3_hat	100	0	0.987	0.208	0.523	0.976	1.566
gamma0_hat	100	0	3.049	1.067	0.921	3.128	6.887
gamma1_hat	100	0	2.505	18.837	−17.852	0.968	182.637
gamma2_hat	100	0	0.766	0.179	0.311	0.749	1.108
gamma3_hat	100	0	0.800	0.144	0.399	0.805	1.159
theta_hat	100	0	−0.377	7.777	−72.026	0.070	15.912
theta_hat_t_stats	100	0	0.130	1.068	−2.878	0.113	2.575
R2_demand	100	0	0.125	0.446	−2.641	0.237	0.556
R2_supply	100	0	0.987	0.003	0.978	0.988	0.993

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.942	0.620	8.837	9.822	12.284
alpha1_hat	100	0	1.077	0.863	−0.684	1.102	5.283
alpha2_hat	100	0	0.089	0.076	−0.161	0.093	0.261
alpha3_hat	100	0	0.994	0.148	0.680	0.990	1.396
gamma0_hat	100	0	2.151	0.852	0.040	2.256	4.073
gamma1_hat	100	0	0.290	4.025	−24.751	0.682	12.127
gamma2_hat	100	0	0.867	0.138	0.527	0.860	1.188
gamma3_hat	100	0	0.881	0.116	0.648	0.878	1.175
theta_hat	100	0	0.670	2.089	−5.121	0.333	13.268
theta_hat_t_stats	100	0	0.565	1.047	−2.419	0.605	3.498
R2_demand	100	0	0.200	0.209	−0.678	0.235	0.613
R2_supply	100	0	0.985	0.003	0.972	0.986	0.990

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.972	0.468	8.912	9.949	10.966
alpha1_hat	100	0	0.955	0.510	−0.215	0.908	2.705
alpha2_hat	100	0	0.102	0.050	−0.020	0.098	0.219
alpha3_hat	100	0	0.983	0.101	0.773	0.981	1.267
gamma0_hat	100	0	1.668	0.585	0.409	1.738	3.122
gamma1_hat	100	0	0.861	2.417	−5.738	0.702	19.291
gamma2_hat	100	0	0.925	0.089	0.659	0.913	1.124
gamma3_hat	100	0	0.927	0.083	0.777	0.923	1.122
theta_hat	100	0	0.438	1.374	−9.967	0.513	5.035
theta_hat_t_stats	100	0	0.940	1.055	−2.898	1.075	3.728
R2_demand	100	0	0.188	0.151	−0.202	0.204	0.447
R2_supply	100	0	0.983	0.003	0.974	0.983	0.989

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.992	0.197	9.598	9.982	10.443
alpha1_hat	100	0	0.975	0.235	0.360	0.962	1.452
alpha2_hat	100	0	0.102	0.023	0.059	0.100	0.187
alpha3_hat	100	0	1.001	0.046	0.915	0.997	1.101
gamma0_hat	100	0	1.174	0.290	0.388	1.167	1.863
gamma1_hat	100	0	0.947	0.484	−0.375	0.927	2.100
gamma2_hat	100	0	0.982	0.043	0.889	0.981	1.108
gamma3_hat	100	0	0.978	0.048	0.865	0.979	1.125
theta_hat	100	0	0.490	0.262	−0.091	0.461	1.218
theta_hat_t_stats	100	0	2.204	0.993	−0.477	2.163	4.211
R2_demand	100	0	0.195	0.066	0.021	0.200	0.320
R2_supply	100	0	0.981	0.001	0.977	0.981	0.984

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.008	0.139	9.666	10.013	10.278
alpha1_hat	100	0	0.995	0.176	0.583	0.985	1.451
alpha2_hat	100	0	0.101	0.017	0.064	0.102	0.144
alpha3_hat	100	0	1.005	0.030	0.930	1.005	1.080
gamma0_hat	100	0	1.027	0.214	0.541	1.047	1.539
gamma1_hat	100	0	0.840	0.353	−0.096	0.893	1.441
gamma2_hat	100	0	0.998	0.034	0.927	0.997	1.073
gamma3_hat	100	0	0.994	0.031	0.926	0.993	1.099
theta_hat	100	0	0.572	0.176	0.228	0.553	1.023
theta_hat_t_stats	100	0	3.694	0.863	1.614	3.656	5.705
R2_demand	100	0	0.202	0.041	0.083	0.205	0.277
R2_supply	100	0	0.980	0.001	0.978	0.980	0.982

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.005	0.084	9.802	10.012	10.204
alpha1_hat	100	0	1.022	0.106	0.801	1.032	1.255
alpha2_hat	100	0	0.098	0.010	0.077	0.098	0.123
alpha3_hat	100	0	1.001	0.021	0.945	0.999	1.046
gamma0_hat	100	0	1.025	0.139	0.685	1.037	1.325
gamma1_hat	100	0	0.897	0.236	0.396	0.890	1.429
gamma2_hat	100	0	0.997	0.020	0.956	0.997	1.054
gamma3_hat	100	0	0.995	0.019	0.950	0.994	1.050
theta_hat	100	0	0.545	0.119	0.287	0.561	0.793
theta_hat_t_stats	100	0	5.573	1.012	3.279	5.605	7.761
R2_demand	100	0	0.200	0.028	0.140	0.198	0.277
R2_supply	100	0	0.980	0.001	0.978	0.980	0.982

\(\alpha_2 = 0.5\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.918	1.030	7.960	9.700	14.079
alpha1_hat	100	0	0.635	2.503	−4.577	0.383	7.811
alpha2_hat	100	0	0.522	0.295	−0.166	0.537	1.309
alpha3_hat	100	0	0.993	0.217	0.623	0.971	1.780
gamma0_hat	100	0	2.870	0.898	0.388	2.973	4.710
gamma1_hat	100	0	−1.060	14.170	−101.261	0.756	27.039
gamma2_hat	100	0	0.783	0.154	0.470	0.767	1.221
gamma3_hat	100	0	0.774	0.149	0.484	0.769	1.356
theta_hat	100	0	0.590	2.925	−5.001	0.158	23.862
theta_hat_t_stats	100	0	0.379	1.037	−2.416	0.363	2.735
R2_demand	100	0	0.262	0.375	−1.820	0.348	0.696
R2_supply	100	0	0.984	0.004	0.971	0.984	0.993

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.042	0.710	8.658	9.920	12.798
alpha1_hat	100	0	1.142	1.940	−3.704	0.923	7.108
alpha2_hat	100	0	0.494	0.197	−0.054	0.486	1.028
alpha3_hat	100	0	1.019	0.154	0.644	1.032	1.481
gamma0_hat	100	0	2.202	0.746	−0.142	2.233	3.695
gamma1_hat	100	0	0.288	5.557	−19.952	0.912	38.596
gamma2_hat	100	0	0.871	0.126	0.559	0.860	1.286
gamma3_hat	100	0	0.864	0.116	0.570	0.873	1.291
theta_hat	100	0	0.400	0.918	−5.588	0.319	3.396
theta_hat_t_stats	100	0	0.927	0.983	−2.089	0.931	2.871
R2_demand	100	0	0.260	0.243	−1.117	0.336	0.554
R2_supply	100	0	0.982	0.004	0.964	0.982	0.989

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.008	0.452	9.236	9.951	11.002
alpha1_hat	100	0	0.901	1.288	−2.563	0.945	4.009
alpha2_hat	100	0	0.511	0.126	0.169	0.517	0.786
alpha3_hat	100	0	0.992	0.093	0.735	0.992	1.356
gamma0_hat	100	0	1.617	0.599	0.238	1.554	3.069
gamma1_hat	100	0	0.557	1.828	−8.838	0.664	5.145
gamma2_hat	100	0	0.930	0.094	0.733	0.939	1.271
gamma3_hat	100	0	0.925	0.099	0.718	0.926	1.221
theta_hat	100	0	0.468	0.351	−0.176	0.437	2.075
theta_hat_t_stats	100	0	1.752	0.924	−0.354	1.844	3.630
R2_demand	100	0	0.270	0.137	−0.168	0.277	0.526
R2_supply	100	0	0.979	0.003	0.969	0.980	0.987

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.985	0.190	9.511	9.980	10.607
alpha1_hat	100	0	1.057	0.577	−0.562	1.106	2.106
alpha2_hat	100	0	0.492	0.063	0.370	0.482	0.652
alpha3_hat	100	0	0.997	0.045	0.884	0.996	1.102
gamma0_hat	100	0	1.081	0.337	0.045	1.102	2.166
gamma1_hat	100	0	0.654	0.756	−1.054	0.659	2.111
gamma2_hat	100	0	0.990	0.050	0.797	0.987	1.131
gamma3_hat	100	0	0.992	0.046	0.869	0.986	1.137
theta_hat	100	0	0.547	0.123	0.288	0.563	0.914
theta_hat_t_stats	100	0	4.658	0.879	2.677	4.746	7.057
R2_demand	100	0	0.292	0.056	0.164	0.300	0.415
R2_supply	100	0	0.977	0.002	0.972	0.977	0.982

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.997	0.154	9.672	9.988	10.373
alpha1_hat	100	0	0.951	0.370	0.116	0.988	2.276
alpha2_hat	100	0	0.505	0.040	0.409	0.505	0.618
alpha3_hat	100	0	1.001	0.034	0.914	0.997	1.070
gamma0_hat	100	0	1.000	0.229	0.470	1.005	1.445
gamma1_hat	100	0	0.830	0.522	−0.450	0.771	1.838
gamma2_hat	100	0	1.001	0.035	0.931	1.003	1.079
gamma3_hat	100	0	1.000	0.036	0.906	1.000	1.085
theta_hat	100	0	0.528	0.092	0.333	0.538	0.718
theta_hat_t_stats	100	0	6.607	0.939	4.465	6.728	9.102
R2_demand	100	0	0.286	0.046	0.149	0.289	0.386
R2_supply	100	0	0.977	0.001	0.973	0.977	0.979

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.001	0.085	9.719	10.004	10.156
alpha1_hat	100	0	1.011	0.213	0.549	1.025	1.559
alpha2_hat	100	0	0.499	0.024	0.432	0.501	0.555
alpha3_hat	100	0	0.998	0.019	0.940	0.999	1.048
gamma0_hat	100	0	1.003	0.146	0.521	1.007	1.290
gamma1_hat	100	0	0.956	0.341	−0.212	1.008	1.794
gamma2_hat	100	0	1.000	0.022	0.956	1.000	1.053
gamma3_hat	100	0	1.000	0.021	0.940	0.997	1.068
theta_hat	100	0	0.506	0.064	0.356	0.502	0.703
theta_hat_t_stats	100	0	10.026	1.026	7.377	9.952	13.464
R2_demand	100	0	0.287	0.024	0.233	0.286	0.368
R2_supply	100	0	0.976	0.001	0.974	0.976	0.978

\(\alpha_2 = 1.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.025	1.054	8.416	9.819	13.799
alpha1_hat	100	0	1.174	4.966	−12.688	0.825	25.156
alpha2_hat	100	0	0.989	0.588	−0.632	0.949	2.952
alpha3_hat	100	0	1.004	0.258	0.489	0.952	1.923
gamma0_hat	100	0	2.822	1.059	−0.520	2.882	5.524
gamma1_hat	100	0	−4.686	26.379	−203.212	1.205	17.270
gamma2_hat	100	0	0.811	0.174	0.304	0.794	1.318
gamma3_hat	100	0	0.793	0.159	0.446	0.793	1.268
theta_hat	100	0	0.770	2.738	−0.908	0.178	23.289
theta_hat_t_stats	100	0	0.500	1.008	−2.223	0.536	3.267
R2_demand	100	0	0.275	0.424	−2.122	0.397	0.744
R2_supply	100	0	0.984	0.004	0.971	0.984	0.992

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.014	0.683	8.583	9.864	12.234
alpha1_hat	100	0	0.899	2.964	−7.428	0.718	8.488
alpha2_hat	100	0	1.017	0.314	0.322	1.005	2.141
alpha3_hat	100	0	0.993	0.136	0.714	0.979	1.387
gamma0_hat	100	0	2.043	0.741	0.487	1.998	4.197
gamma1_hat	100	0	0.100	3.856	−12.010	1.170	6.557
gamma2_hat	100	0	0.888	0.121	0.615	0.905	1.157
gamma3_hat	100	0	0.883	0.115	0.614	0.879	1.164
theta_hat	100	0	0.397	0.387	−0.322	0.317	1.903
theta_hat_t_stats	100	0	1.186	0.941	−1.134	1.157	3.407
R2_demand	100	0	0.304	0.191	−0.249	0.329	0.608
R2_supply	100	0	0.981	0.003	0.971	0.982	0.987

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.052	0.488	8.847	10.022	11.306
alpha1_hat	100	0	1.198	2.177	−3.931	1.367	6.972
alpha2_hat	100	0	0.993	0.241	0.512	0.976	1.761
alpha3_hat	100	0	1.016	0.106	0.780	1.002	1.317
gamma0_hat	100	0	1.508	0.594	−0.358	1.580	2.746
gamma1_hat	100	0	0.013	2.722	−7.193	0.628	5.311
gamma2_hat	100	0	0.939	0.088	0.748	0.924	1.234
gamma3_hat	100	0	0.944	0.090	0.769	0.926	1.167
theta_hat	100	0	0.511	0.301	−0.102	0.470	1.428
theta_hat_t_stats	100	0	2.084	0.929	−0.529	2.062	4.203
R2_demand	100	0	0.293	0.138	−0.167	0.305	0.528
R2_supply	100	0	0.978	0.004	0.965	0.979	0.985

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.032	0.204	9.599	10.041	10.669
alpha1_hat	100	0	1.042	0.942	−1.293	1.059	3.488
alpha2_hat	100	0	1.005	0.111	0.657	1.021	1.303
alpha3_hat	100	0	1.004	0.041	0.910	1.006	1.118
gamma0_hat	100	0	1.009	0.327	0.150	1.060	1.912
gamma1_hat	100	0	0.651	1.112	−2.178	0.746	4.315
gamma2_hat	100	0	0.997	0.051	0.892	0.993	1.138
gamma3_hat	100	0	0.998	0.040	0.870	0.999	1.091
theta_hat	100	0	0.529	0.121	0.185	0.524	0.945
theta_hat_t_stats	100	0	5.103	0.866	2.109	5.107	6.784
R2_demand	100	0	0.313	0.053	0.145	0.312	0.413
R2_supply	100	0	0.975	0.002	0.969	0.975	0.980

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.032	0.154	9.640	10.025	10.500
alpha1_hat	100	0	1.070	0.659	−0.595	0.976	2.432
alpha2_hat	100	0	1.003	0.079	0.770	1.007	1.191
alpha3_hat	100	0	1.005	0.031	0.933	1.000	1.081
gamma0_hat	100	0	0.993	0.241	0.417	1.010	1.598
gamma1_hat	100	0	0.752	0.863	−1.277	0.728	2.790
gamma2_hat	100	0	1.004	0.034	0.921	1.002	1.075
gamma3_hat	100	0	1.000	0.031	0.911	1.002	1.082
theta_hat	100	0	0.518	0.083	0.272	0.516	0.694
theta_hat_t_stats	100	0	7.195	0.935	4.613	7.164	9.484
R2_demand	100	0	0.313	0.042	0.214	0.318	0.400
R2_supply	100	0	0.975	0.002	0.971	0.975	0.980

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.987	0.095	9.744	9.980	10.205
alpha1_hat	100	0	0.971	0.444	−0.180	0.945	2.023
alpha2_hat	100	0	0.998	0.049	0.888	0.999	1.115
alpha3_hat	100	0	0.996	0.021	0.948	0.993	1.054
gamma0_hat	100	0	1.025	0.139	0.714	0.999	1.386
gamma1_hat	100	0	0.923	0.428	−0.014	0.904	1.899
gamma2_hat	100	0	0.996	0.021	0.944	0.998	1.064
gamma3_hat	100	0	0.997	0.021	0.948	0.995	1.053
theta_hat	100	0	0.506	0.044	0.385	0.505	0.623
theta_hat_t_stats	100	0	11.252	0.750	9.289	11.281	12.920
R2_demand	100	0	0.320	0.025	0.255	0.319	0.366
R2_supply	100	0	0.975	0.001	0.973	0.975	0.977

\(\alpha_2 = 5.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.905	0.857	7.903	9.839	13.046
alpha1_hat	100	0	1.229	19.905	−56.477	−1.308	46.467
alpha2_hat	100	0	4.838	2.291	−0.843	5.057	11.967
alpha3_hat	100	0	0.994	0.178	0.653	0.978	1.503
gamma0_hat	100	0	2.697	1.091	−0.526	2.753	4.874
gamma1_hat	100	0	−7.803	161.793	−846.570	−2.044	1171.309
gamma2_hat	100	0	0.815	0.184	0.394	0.822	1.209
gamma3_hat	100	0	0.823	0.161	0.349	0.815	1.322
theta_hat	100	0	0.377	4.604	−34.915	0.324	21.124
theta_hat_t_stats	100	0	0.674	1.082	−2.379	0.964	2.865
R2_demand	100	0	0.355	0.287	−1.042	0.408	0.736
R2_supply	100	0	0.983	0.004	0.969	0.983	0.991

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.060	0.675	8.425	10.004	12.044
alpha1_hat	100	0	0.282	13.587	−33.200	−1.095	43.051
alpha2_hat	100	0	5.147	1.474	0.676	5.129	9.030
alpha3_hat	100	0	0.999	0.156	0.745	0.993	1.553
gamma0_hat	100	0	2.160	0.805	−0.636	2.280	4.232
gamma1_hat	100	0	−1.724	22.473	−183.848	0.780	28.859
gamma2_hat	100	0	0.869	0.132	0.541	0.858	1.239
gamma3_hat	100	0	0.864	0.122	0.573	0.867	1.102
theta_hat	100	0	0.369	0.455	−0.263	0.336	3.938
theta_hat_t_stats	100	0	1.124	0.820	−1.195	1.208	2.909
R2_demand	100	0	0.312	0.260	−0.988	0.370	0.586
R2_supply	100	0	0.980	0.004	0.966	0.980	0.986

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.960	0.473	8.789	9.966	11.243
alpha1_hat	100	0	−0.095	9.647	−19.686	0.279	20.684
alpha2_hat	100	0	5.058	1.106	2.841	4.852	8.631
alpha3_hat	100	0	0.994	0.114	0.770	0.985	1.251
gamma0_hat	100	0	1.495	0.706	−1.429	1.475	3.526
gamma1_hat	100	0	−2.369	11.519	−42.349	−0.872	21.932
gamma2_hat	100	0	0.941	0.105	0.676	0.938	1.304
gamma3_hat	100	0	0.945	0.115	0.713	0.914	1.297
theta_hat	100	0	0.496	0.253	−0.025	0.456	1.478
theta_hat_t_stats	100	0	2.369	0.932	−0.134	2.305	4.479
R2_demand	100	0	0.342	0.130	−0.090	0.361	0.561
R2_supply	100	0	0.977	0.004	0.959	0.977	0.985

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.016	0.184	9.555	10.003	10.435
alpha1_hat	100	0	1.571	3.895	−7.121	1.534	10.478
alpha2_hat	100	0	4.965	0.453	3.772	4.948	5.792
alpha3_hat	100	0	1.003	0.043	0.913	1.002	1.110
gamma0_hat	100	0	1.091	0.272	0.313	1.085	1.673
gamma1_hat	100	0	−1.295	4.697	−12.273	−1.650	10.414
gamma2_hat	100	0	0.991	0.040	0.900	0.994	1.120
gamma3_hat	100	0	0.985	0.042	0.874	0.984	1.101
theta_hat	100	0	0.529	0.098	0.253	0.531	0.715
theta_hat_t_stats	100	0	5.649	0.864	3.361	5.640	7.545
R2_demand	100	0	0.341	0.053	0.182	0.347	0.431
R2_supply	100	0	0.975	0.002	0.969	0.975	0.979

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.005	0.139	9.680	10.007	10.451
alpha1_hat	100	0	1.166	2.547	−3.731	0.902	6.745
alpha2_hat	100	0	4.994	0.341	4.223	5.031	5.811
alpha3_hat	100	0	1.004	0.034	0.927	1.005	1.089
gamma0_hat	100	0	1.029	0.201	0.529	1.035	1.626
gamma1_hat	100	0	−0.547	3.412	−10.827	−0.504	8.409
gamma2_hat	100	0	0.996	0.028	0.902	0.995	1.071
gamma3_hat	100	0	0.995	0.029	0.880	0.997	1.045
theta_hat	100	0	0.525	0.083	0.321	0.529	0.731
theta_hat_t_stats	100	0	7.982	0.974	5.001	8.028	10.732
R2_demand	100	0	0.344	0.042	0.237	0.346	0.452
R2_supply	100	0	0.974	0.001	0.970	0.974	0.977

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.000	0.085	9.800	10.005	10.220
alpha1_hat	100	0	0.678	1.526	−2.974	0.854	3.926
alpha2_hat	100	0	5.032	0.195	4.544	5.025	5.640
alpha3_hat	100	0	0.998	0.018	0.954	1.001	1.045
gamma0_hat	100	0	0.993	0.142	0.659	0.993	1.310
gamma1_hat	100	0	0.922	1.897	−4.592	0.726	4.979
gamma2_hat	100	0	1.001	0.021	0.951	1.000	1.051
gamma3_hat	100	0	1.000	0.019	0.961	0.997	1.048
theta_hat	100	0	0.503	0.045	0.394	0.505	0.645
theta_hat_t_stats	100	0	12.348	0.867	10.498	12.312	14.451
R2_demand	100	0	0.348	0.023	0.293	0.348	0.397
R2_supply	100	0	0.974	0.001	0.971	0.974	0.976

\(\alpha_2 = 20.0\)

\(n = 50\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.952	1.012	8.115	9.864	13.583
alpha1_hat	100	0	−6.081	81.140	−175.858	−5.806	224.524
alpha2_hat	100	0	20.447	8.570	−2.178	20.765	39.275
alpha3_hat	100	0	0.966	0.235	0.550	0.939	1.762
gamma0_hat	100	0	2.911	1.150	−1.406	3.069	5.667
gamma1_hat	100	0	−201.496	1479.822	−14641.636	−16.661	133.864
gamma2_hat	100	0	0.793	0.188	0.356	0.771	1.491
gamma3_hat	100	0	0.798	0.173	0.458	0.783	1.238
theta_hat	100	0	1.360	8.445	−0.668	0.271	83.274
theta_hat_t_stats	100	0	0.673	1.151	−2.623	0.777	3.126
R2_demand	100	0	0.319	0.389	−1.852	0.434	0.806
R2_supply	100	0	0.983	0.005	0.954	0.984	0.991

\(n = 100\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.919	0.624	8.551	9.892	12.815
alpha1_hat	100	0	3.180	50.544	−105.249	3.688	130.740
alpha2_hat	100	0	19.360	6.359	5.189	18.479	43.643
alpha3_hat	100	0	1.000	0.152	0.649	0.982	1.449
gamma0_hat	100	0	2.153	0.689	0.240	2.147	3.507
gamma1_hat	100	0	−20.328	61.971	−224.774	−7.449	91.478
gamma2_hat	100	0	0.873	0.111	0.634	0.867	1.208
gamma3_hat	100	0	0.871	0.121	0.614	0.857	1.168
theta_hat	100	0	0.438	0.365	−0.215	0.400	1.501
theta_hat_t_stats	100	0	1.387	0.972	−0.904	1.351	3.698
R2_demand	100	0	0.351	0.274	−1.872	0.380	0.676
R2_supply	100	0	0.980	0.004	0.968	0.980	0.987

\(n = 200\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.013	0.473	8.633	9.987	11.164
alpha1_hat	100	0	0.905	38.348	−127.127	7.208	71.531
alpha2_hat	100	0	20.126	4.806	9.769	19.467	38.683
alpha3_hat	100	0	1.013	0.100	0.800	1.018	1.314
gamma0_hat	100	0	1.522	0.653	−0.903	1.586	2.669
gamma1_hat	100	0	−14.090	39.473	−124.585	−11.299	63.808
gamma2_hat	100	0	0.934	0.103	0.701	0.938	1.214
gamma3_hat	100	0	0.946	0.104	0.723	0.943	1.264
theta_hat	100	0	0.505	0.266	0.001	0.475	1.438
theta_hat_t_stats	100	0	2.370	0.924	0.009	2.382	4.915
R2_demand	100	0	0.326	0.140	−0.064	0.359	0.547
R2_supply	100	0	0.977	0.004	0.963	0.977	0.984

\(n = 1000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.992	0.192	9.555	9.974	10.513
alpha1_hat	100	0	2.092	14.772	−39.193	3.266	45.123
alpha2_hat	100	0	19.835	1.710	14.689	19.769	23.925
alpha3_hat	100	0	1.002	0.042	0.916	0.996	1.100
gamma0_hat	100	0	1.089	0.288	0.195	1.083	1.999
gamma1_hat	100	0	−3.879	16.591	−46.964	−3.304	34.530
gamma2_hat	100	0	0.989	0.043	0.878	0.990	1.119
gamma3_hat	100	0	0.996	0.048	0.896	0.991	1.134
theta_hat	100	0	0.512	0.096	0.296	0.520	0.734
theta_hat_t_stats	100	0	5.585	0.840	3.557	5.620	7.244
R2_demand	100	0	0.356	0.048	0.230	0.362	0.464
R2_supply	100	0	0.974	0.002	0.968	0.974	0.978

\(n = 2000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	9.992	0.192	9.555	9.974	10.513
alpha1_hat	100	0	2.092	14.772	−39.193	3.266	45.123
alpha2_hat	100	0	19.835	1.710	14.689	19.769	23.925
alpha3_hat	100	0	1.002	0.042	0.916	0.996	1.100
gamma0_hat	100	0	1.089	0.288	0.195	1.083	1.999
gamma1_hat	100	0	−3.879	16.591	−46.964	−3.304	34.530
gamma2_hat	100	0	0.989	0.043	0.878	0.990	1.119
gamma3_hat	100	0	0.996	0.048	0.896	0.991	1.134
theta_hat	100	0	0.512	0.096	0.296	0.520	0.734
theta_hat_t_stats	100	0	5.585	0.840	3.557	5.620	7.244
R2_demand	100	0	0.356	0.048	0.230	0.362	0.464
R2_supply	100	0	0.974	0.002	0.968	0.974	0.978

\(n = 5000\)

	Unique (#)	Missing (%)	Mean	SD	Min	Median	Max
group_id_k	100	0	50.500	29.011	1.000	50.500	100.000
alpha0_hat	100	0	10.007	0.089	9.789	10.003	10.203
alpha1_hat	100	0	0.465	6.336	−19.340	0.529	15.995
alpha2_hat	100	0	20.081	0.789	18.157	20.126	22.977
alpha3_hat	100	0	1.002	0.019	0.961	1.000	1.045
gamma0_hat	100	0	1.012	0.134	0.715	1.018	1.321
gamma1_hat	100	0	−1.800	7.541	−27.611	−1.720	13.695
gamma2_hat	100	0	0.999	0.020	0.952	0.999	1.051
gamma3_hat	100	0	0.999	0.021	0.948	0.998	1.053
theta_hat	100	0	0.511	0.046	0.430	0.510	0.640
theta_hat_t_stats	100	0	12.775	0.871	10.778	12.748	14.861
R2_demand	100	0	0.356	0.021	0.296	0.357	0.399
R2_supply	100	0	0.974	0.001	0.970	0.974	0.976

Plot

iv_polynomial

50

## Warning: Removed 4 rows containing missing values (`geom_col()`).

100 200 1000

## Warning: Removed 1 rows containing missing values (`geom_col()`).

2000 5000 10000